rational approximation solution of the fractional sharma tasso olever equation in the paper we implement relatively new analytical techniques the variational iteration method the adomian decomposition method and the homotopy perturbation method for obtaining a rational approximation solution of the fractional sharma tasso olever equation the three methods in applied mathematics can be used as alternative methods for obtaining an analytic and approximate solution for different types of differential equations in these schemes the solution takes the form of a convergent series with easily computable components the numerical results demonstrate the significant features efficiency and reliability of the three approaches

analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi ld m controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of nonlinear dynamic system containing fractional derivative ji zeng wang et al coiflets based method in the solution of nonlinear dynamic system containing fractional derivative in the fourth international conference on nonlinear mechanics icnm iv shanghai august 2002 pp 1304 1308 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with the exact solution a good agreement of the results is observed

comparing numerical methods for helmholtz equation model problem in this article we implement a relatively new numerical technique adomian s decomposition method for solving the linear helmholtz partial differential equations the method in applied mathematics can be an effective procedure to obtain for the analytic and approximate solutions a new approach to a linear or nonlinear problems is particularly valuable as a tool for scientists and applied mathematicians because it provides immediate and visible symbolic terms of analytic solution as well as its numerical approximate solution to both linear and nonlinear problems without linearization solving frontier problems of physics the decomposition method kluwer academic publishers boston 1994 j math anal appl 35 1988 501 it does also not require discretization and consequently massive computation in this scheme the solution is performed in the form of a convergent power series with easily computable components this paper will present a numerical comparison with the adomian decomposition and a conventional finite difference method the numerical results demonstrate that the new method is quite accurate and readily implemented

adomian decomposition a tool for solving a system of fractional differential equations abstract adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations convergence of the method has been discussed with some illustrative examples in particular for the initial value problem d 1 y 1 d n y n t a y 1 y n t y i 0 c i i 1 n where a a i j is a real square matrix the solution turns out to be y x e 1 n 1 x 1 a 1 x n a n y 0 where e 1 n 1 denotes multivariate mittag leffler function defined for matrix arguments and a i is the matrix having ith row as a i 1 a i n and all other entries are zero fractional oscillation and bagley torvik equations are solved as illustrative examples

a pathwise ergodic theorem for quantum trajectories if the time evolution of an open quantum system approaches equilibrium in the time mean then on any single trajectory of any of its unravellings the time averaged state approaches the same equilibrium state with probability 1 in the case of multiple equilibrium states the quantum trajectory converges in the mean to a random choice from these states

solving delay differential systems with history functions by the adomian decomposition method abstract a number of nonlinear phenomena in many branches of the applied sciences and engineering are described in terms of delay differential equations which arise when the evolution of a system depends both on its present and past time in this work we apply the adomian decomposition method adm to obtain solutions of several delay differential equations subject to history functions and then investigate several numerical examples via our subroutines in maple that demonstrate the efficiency of our new approach in our approach history functions are continuous across the initial value and its derivatives must be equal to the initial conditions see section 3 so that our results are more efficient and accurate than previous works

the solution of two dimensional nonlinear differential equation by the adomian decomposition method in this paper the adomian s decomposition method is used to investigate nonlinear two dimensional wave equation the analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components the nonhomogenous equation is effectively solved by employing the phenomena of the self canceling noise terms where sum of components vanishes in the limit comparing the methodology with some known techniques shows that the present approach is powerful and reliable its remarkable accuracy properties are finally demonstrated by an example

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

a new computational method for volterra fredholm integral equations abstract the main purpose of this article is to demonstrate the use of the adomian decomposition method for mixed nonlinear volterra fredholm integral equations a bound is also given for the adomian decomposition series finally numerical examples are presented to illustrate the implementation and accuracy of the decomposition method

inefficiency of nash equilibria it is shown that nash equilibria of smooth games generally tend to be inefficient in the pareto sense

an implementation of the adm for generalized one dimensional klein gordon equation in this study a decomposition method for approximating the solution of the generalized one dimensional klein gordon equation is implemented to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solution

adomian decomposition method with green s function for sixth order boundary value problems in this paper the adomian decomposition method with green s function is applied to solve linear and nonlinear sixth order boundary value problems the numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the decomposition method is of high accuracy more convenient and efficient for solving high order boundary value problems

an artificial parameter decomposition method for nonlinear oscillators applications to oscillators with odd nonlinearities abstract a method for obtaining series solutions of nonlinear second order ordinary differential equations based on the introduction of an artificial parameter is presented and shown to be identical to the well known adomian s decomposition technique the method is formulated in both integral and differential forms for the determination of the limit cycle of oscillators with odd nonlinearities two differential forms and one integral form of the artificial parameter method are presented these versions are based on introducing a linear stiffness term with an unknown frequency and the use of either the original independent variable or a new independent variable that depends linearly on the unknown frequency of the oscillator the three formulations provide identical results and their application to eight oscillators with odd nonlinearities shows that the artificial parameter technique presented in this paper predicts the same frequency of oscillation as the harmonic balance and iterative techniques as well as modified linstedt poincare methods however the method presented here is based on the introduction of an artificial parameter and does not require the presence of small perturbation parameters in the ordinary differential equation it is also shown that two and three level iterative methods yield the same frequency of oscillation as the artificial parameter technique presented in this paper provided that the initial iterate of the former coincides with the leading order solution of the latter and only one iteration of iterative techniques and only the second approximation of the artificial parameter method are determined

the adomian decomposition method in turning point problems in this paper the decomposition method is applied to boundary value problems of ordinary differential equations with a parameter exhibiting turning points

fast fair and efficient flows in networks we study the problem of minimizing the maximum latency of flows in networks with congestion we show that this problem is np hard even when all arc latency functions are linear and there is a single source and sink still an optimal flow and an equilibrium flow share a desirable property in this situation all flow carrying paths have the same length i e these solutions are fair which is in general not true for optimal flows in networks with nonlinear latency functions in addition the maximum latency of the nash equilibrium which can be computed efficiently is within a constant factor of that of an optimal solution that is the so called price of anarchy is bounded in contrast we present a family of instances with multiple sources and a single sink for which the price of anarchy is unbounded even in networks with linear latencies furthermore we show that an s t flow that is optimal with respect to the average latency objective is near optimal for the maximum latency objective and it is close to being fair conversely the average latency of a flow minimizing the maximum latency is also within a constant factor of that of a flow minimizing the average latency

adomian decomposition method for solving bvps for fourth order integro differential equations the adomian decomposition method adm is applied to solve both linear and nonlinear boundary value problems bvps for fourth order integro differential equations the numerical results obtained with minimum amount of computation or mathematics compare reasonably well with exact solutions

a new iterative method for solving nonlinear equations abstract in this paper we present a new efficient iterative method for solving nonlinear equations improving newton raphson method this method is based on a modification of the proposal of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method appl math comput 145 2003 887 893 the convergence properties of the method and some other methods are discussed some numerical illustrations are given to show that the proposed method behaves equal or better performance compared to the other methods of same kind

a numerical solution and an exact explicit solution of the nls equation we consider traveling wave solutions of the nonlinear schrodinger nls for short equation in this paper by considering the decomposition scheme we first obtain the exact solutions of the nls equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some initial values of the nls equation

the decomposition method for stiff systems of ordinary differential equations in this paper the decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases focusing our interest in stiff problems

revised adomian decomposition method for solving systems of ordinary and fractional differential equations a modification of the adomian decomposition method applied to systems of linear nonlinear ordinary and fractional differential equations which yields a series solution with accelerated convergence has been presented illustrative examples have been given

comparison of the solutions obtained by b spline fem and adm of kdv equation a numerical solution to a generalized korteweg de vries kdv equation is obtained using the galerkin method with quadratic b spline finite element method fem over which the nonlinear term is locally linearized and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

the price of anarchy under nonlinear and asymmetric costs in this paper we characterize the price of anarchy i e the inefficiency between user and system optimal solutions when costs are nonseparable asymmetric and nonlinear generalizing earlier work that has addressed the price of anarchy under separable costs the results in this paper apply primarily to nonatomic games such as the traffic equilibrium problem but also in competitive multiperiod pricing and competitive supply chain settings the bounds established in this paper are tight and explicitly account for the degree of asymmetry and nonlinearity of the cost function we first provide a proof method for problems with a positive definite jacobian matrix subsequently we use ideas from semidefinite optimization in order to account for problems with a positive semidefinite jacobian matrix where the first approach does not apply this latter connection also provides a different application of semidefinite optimization

adomian decomposition method for solution of differential algebraic equations solutions of differential algebraic equations is considered by adomian decomposition method in e babolian m m hosseini reducing index and spectral methods for differential algebraic equations j appl math comput 140 2003 77 and m m hosseini an index reduction method for linear hessenberg systems j appl math comput in press an efficient technique to reduce index of semi explicit differential algebraic equations has been presented in this paper adomian decomposition method is applied to reduced index problems the scheme is tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

identifying a control function in parabolic partial differential equations from overspecified boundary data determination of an unknown time dependent function in parabolic partial differential equations plays a very important role in many branches of science and engineering in the current investigation the adomian decomposition method is used for finding a control parameter p t in the quasilinear parabolic equation u t u x x p t email protected in 0 1 x 0 t with known initial and boundary conditions and subject to an additional condition in the form of 0 1k x u x t dx e t email protected email protected t which is called the boundary integral overspecification the main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known adomian decomposition method the decomposition procedure of adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form furthermore due to the rapid convergence of adomian s method a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution this method provides a reliable algorithm that requires less work if compared with the traditional techniques some illustrative examples are presented to show the efficiency of the presented method

decomposition method for solving a system of fourth order obstacle boundary value problems in this paper we present a fast and accurate numerical scheme for the solution of a system of fourth order boundary value problems associated with obstacle unilateral and contact problems the decomposition method and a modified form of this method are applied to construct the numerical solutions the new approach provides the solution in the form of a rapidly convergent series with easily computable components and not at grid points the scheme is tested on two problems the results demonstrate reliability and efficiency of the algorithm developed

a reliable symbolic implementation of algorithm for calculating adomian polynomials in this paper we introduce a reliable symbolic implementation of the algorithm for calculating adomian polynomials and present some examples to show the simplicity and efficiency of the new method

on the convergence of adomian decomposition method here a simple method to determine the rate of convergence of adomian decomposition method is introduced the proposed method is used to compare between the rate of convergence of standard and modified proposed by wazwaz a m wazwaz a new method for solving singular initial value problems in the second order ordinary differential equations appl math comput 128 2002 45 57 adomian methods for solving lane emden singular problem furthermore with providing some examples the aforementioned cases are dealt with numerically

homotopy perturbation method for fractional fornberg whitham equation this article presents the approximate analytical solutions to solve the nonlinear fornberg whitham equation with fractional time derivative by using initial values the explicit solutions of the equations are solved by using a reliable algorithm like homotopy perturbation method the fractional derivatives are taken in the caputo sense numerical results show that the hpm is easy to implement and accurate when applied to time fractional pdes

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

series solution to the pochhammer chreeequation and comparison with exact solutions in this study a decomposition method for approximating the solution of the pochhammer chreeequation is implemented by using this scheme explicit exact solution is calculated in the form of a convergent power series with easily computable components to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solutions known for some special cases

solving the problem of biological species living together by adomian decomposition method in this paper we use adomian decomposition method for solving the system of nonlinear integro differential equations derived from considering biological species living together

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

application of modified decomposition method for the analytical solution of space fractional diffusion equation abstract spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow finance and others areas of application this paper presents the analytical solutions of the space fractional diffusion equations by modified decomposition method mdm by using initial conditions the explicit solutions of the equations have been presented in the closed form the decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self cancelling noise phenomenon two examples the first one is one dimensional and the second one is two dimensional fractional diffusion equation are presented to show the application of the present technique the present method performs extremely well in terms of efficiency and simplicity

numerical approach to differential equations of fractional order in this paper the variational iteration method and the adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order the two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations in these schemes the solution takes the form of a convergent series with easily computable components this paper presents a numerical comparison between the two methods for solving systems of fractional differential equations numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order

an algorithm for adomian decomposition method in this paper a reliable technique for calculating adomian polynomials for nonlinear operators is developed the algorithm is fulfilled with symbolic computation so that the adomian decomposition methods for solving differential equations can be mechanized in maple ten examples are presented to illustrate the implementation of the program

comments on a new algorithm for solving classical blasius equation by l wang abstract in a recent paper wang l wang a new algorithm for solving classical blasius equation appl math comput 157 2004 1 9 employed the adomian decomposition method adm to solve numerically the famous blasius equation the purpose of this note is to correct the numerical solution of wang and to present an improved numerical solution using the adm pade approach the numerical result compares reasonably well with the result obtained from a shooting method

an approximate solution of a nonlinear fractional differential equation by adomian decomposition method the aim of the present analysis is to apply adomian decomposition method for the solution of a nonlinear fractional differential equation finally the solution obtained by the decomposition method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method a good agreement of the results is observed

an application of the decompositionmethod for the two dimensional kdv burgers equation a relatively new decomposition method is presented to find the explicit and numerical solutions of the two dimensional korteweg de vries burgers equation tdkdvb for short for the initial conditions some numerical results are also given for this equation by using the decomposition method

an application of the adm to seven order sawada kotara equations we implemented the adomian decomposition method for short adm for approximating the solution of the seventh order sawada kotera for short ssk and a lax s seventh order kdv for short lskdv equations by using this scheme explicit exact solution is calculated we obtain the exact solitary wave solutions and numerical solutions of the lskdv and ssk equations for the initial conditions the numerical solutions are compared with the known analytical solutions their remarkable accuracy are finally demonstrated for the both seven order equations

an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

variational iteration method for the time fractional fornberg whitham equation this paper presents the approximate analytical solutions to solve the nonlinear fornberg whitham equation with fractional time derivative by using initial values explicit solutions of the equations are solved by using a reliable algorithm like the variational iteration method the fractional derivatives are taken in the caputo sense the present method performs extremely well in terms of efficiency and simplicity numerical results for different particular cases of a are presented graphically

adomian s decomposition method and homotopy perturbation method in solving nonlinear equations the adomian s decomposition method and the homotopy perturbation method are two powerful methods which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution by theoretical analysis of the two methods we show in the present paper that the two methods are equivalent in solving nonlinear equations

on experimental results and explicit exact solutions for the generalized boussinesq type equation we implemented a decomposition method for approximating the solution of the generalized boussinesq type equation by using this scheme the explicit exact solution is calculated in the form of a convergent power series with easily computable components to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solution

piecewise homotopy methods for nonlinear ordinary differential equations abstract piecewise homotopy perturbation methods are developed for the solution of nonlinear ordinary differential equations these methods are based on the introduction of an artificial or book keeping parameter and the expansion of the solution in a power series of this parameter and provide analytical solutions in open intervals which are smooth everywhere three piecewise adaptive homotopy perturbation methods based on the use of either a fixed number of approximants and a variable step size a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size are presented and applied to eight nonlinear ordinary differential equations it is shown that piecewise adaptive homotopy perturbation methods predict essentially the same solutions as matlab s variable step variable order solvers and variable order transition matrix techniques provided that five term approximations of the decomposition method are applied to both the displacement and the velocity it is also shown that piecewise homotopy perturbation techniques that use three term approximations to both the displacement and the velocity provide essentially the same results as those obtained with a second order accurate time linearization technique when the same step is employed in both schemes

numerically solution of fuzzy differential equations by adomian method in this paper a method for numerical approximation of fuzzy first order initial value problem is presented buckly and feruing fuzzy sets syst 110 2000 43 have solved fuzzy first order initial value problem they solved problem in crisp case and then extend the solution to fuzzy case in this paper we use adomian method to find the approximate solution in crisp case and extend it to fuzzy case using this method we solve problems that the classical methods could not be applied for them in crisp case

solving multi term linear and non linear diffusion wave equations of fractional order by adomian decomposition method abstract multi term linear and non linear diffusion wave equations of fractional order are solved using adomian decomposition method some numerical examples are presented

numerical method for solving fractional coupled burgers equations in this paper we use the fractional variational iteration method fvim to solve a time and space fractional coupled burgers equations some numerical examples are presented to show the efficiency of considered method a comparison of the proposed method is made with the exact solution adomain decomposition method adm generalized differential transformation method gdtm and homotopy perturbation method hpm

solitary wave solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this letter based on the idea of adomian s decomposition method and with help of mathematica we obtain the exact solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this paper by considering the decomposition scheme we first obtain the exact solutions of these two equation for the initial conditions without using any classical transformations and then their numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions their remarkable accuracy is finally demonstrated in the study of some values p 1 of the compound kdv type and compound kdv burgers type equations

iterative methods improving newton s method by the decomposition method in this paper we present a sequence of iterative methods improving newton s method for solving nonlinear equations the adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses the orders of convergence are derived analytically and then rederived by applying symbolic computation of maple some numerical illustrations are given

an ergodic theorem for quantum counting processes for a quantum mechanical counting process we show ergodicity under the condition that the underlying open quantum system approaches equilibrium in the time mean this implies equality of time average and ensemble average for correlation functions of the detection current to all orders and with probability 1

numerical methods for fourth order fractional integro differential equations this paper outlines a reliable strategy for solving linear and nonlinear boundary value problems for fourth order fractional integro differential equations the fractional derivative is considered in the caputo sense the adomian decomposition method is found to be fast and accurate numerical examples are presented to illustrate the efficiency and reliability of the method

analytical solution of the droplet breakup equation by the adomian decomposition method abstract the droplet population balance equations pbes which despite its importance rarely has an analytical solution however few cases with assumed functional forms of breakup rate daughter droplet distribution exist where most of these solutions are for the batch stirred vessel a new framework for solving pbes for batch and continuous systems is proposed in this work which uses the adomian decomposition method this technique overcomes the crucial difficulties of numerical discretization and stability that often characterize previous solutions in this area the technique used in this work has been tested for the droplet breakup equation the solutions are presented for several cases for which analytical solutions are available for batch and continuous systems for droplet breakup in stirred vessels in all cases the predicted droplet size distributions converge exactly in a continuous form to that of the analytical solution

selfish routing in capacitated networks according to wardrop s first principle agents in a congested network choose their routes selfishly a behavior that is captured by the nash equilibrium of the underlying noncooperative game a nash equilibrium does not optimize any global criterion per se and so there is no apparent reason why it should be close to a solution of minimal total travel time i e the system optimum in this paper we offer positive results on the efficiency of nash equilibria in traffic networks in contrast to prior work we present results for networks with capacities and for latency functions that are nonconvex nondifferentiable and even discontinuous the inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows in this more general model multiple nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient nonetheless our main result shows that the best equilibrium is as efficient as in the model without capacities moreover this holds true for broader classes of travel cost functions than considered hitherto

analytical solution of the bagley torvik equation by adomian decomposition method abstract the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi d controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of bagley torvik equation r l bagley p j torvik on the appearance of the fractional derivative in the behavior of real materials asme j appl mech 51 1984 294 298 i podlubny fractional differential equations academic press san diego ca usa 1999 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with those available in the work of podlubny i podlubny fractional differential equations academic press san diego ca usa 1999 a good agreement of the results is observed

the decomposition method for ordinary differential equations with discontinuities in this paper the decomposition method is applied to the initial value problem ivp for ordinary differential equations with discontinuities for both linear and nonlinear cases

solving a multi order fractional differential equation using adomian decomposition abstract an algorithm has been developed to convert the multi order fractional differential equation d y t f t y t d 1 y t d n y t y k 0 c k k 0 m where m d denotes caputo fractional derivative of order into a system of fractional differential equations further adomian decomposition method has been employed to solve the system of fractional differential equations some illustrative examples are presented

adomian decomposition method for solution of nonlinear differential algebraic equations in m m hosseini adomian decomposition method with chebyshev polynomials appl math comput in press an efficient modification of the adomian decomposition method was presented by using chebyshev polynomials also in m m hosseini adomian decomposition method for solution of differential algebraic equations j comput appl math in press solution of linear differential algebraic equations was considered by adomian decomposition method in this paper standard and modified adomian decomposition methods are applied to non linear differential algebraic equations the schemes are tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

solving a system of nonlinear fractional differential equations using adomian decomposition adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations dxiyi x ni x y1 yn yi k 0 cki 0 k i 1 i n and dxi denotes caputo fractional derivative some examples are solved as illustrations using symbolic computation

exact and numerical traveling wave solutions of whitham broer kaup equations in this paper we find the explicit and numerical traveling wave solutions of whitham broer kaup for short wbk equations which contain blow up solutions and periodic solutions by using the decomposition method by using this method the solutions were calculated in the form of a convergent power series with easily computable components the convergence of the method as applied to the whitham broer kaup equations is illustrated numerically

stackelberg routing in arbitrary networks we investigate the impact of stackelberg routing to reduce the price of anarchy in network routing games in this setting an fraction of the entire demand is first routed centrally according to a predefined stackelberg strategy and the remaining demand is then routed selfishly by nonatomic players although several advances have been made recently in proving that stackelberg routing can in fact significantly reduce the price of anarchy for certain network topologies the central question of whether this holds true in general is still open we answer this question negatively by constructing a family of single commodity instances such that every stackelberg strategy induces a price of anarchy that grows linearly with the size of the network moreover we prove upper bounds on the price of anarchy of the largest latency first llf strategy that only depend on the size of the network besides other implications this rules out the possibility to construct constant size networks to prove an unbounded price of anarchy in light of this negative result we consider bicriteria bounds we develop an efficiently computable stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of 1 1 finally we analyze the effectiveness of an easy to implement stackelberg strategy called scale we prove bounds for a general class of latency functions that includes polynomial latency functions as a special case our analysis is based on an approach that is simple yet powerful enough to obtain almost tight bounds for scale in general networks

adomian decomposition method with chebyshev polynomials in this paper an efficient modification of the adomian decomposition method is presented by using chebyshev polynomials the proposed method can be applied to linear and non linear models the scheme is tested for some examples and the obtained results demonstrate reliability and efficiency of the proposed method

adomian decomposition approach to a sir epidemic model with constant vaccination strategy over the years diligent vaccination campaigns have resulted in high levels of permanent immunity against the childhood disease among the population in this article a sir model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is developed the qualitative analysis reveals the vaccination reproductive number for disease control and eradication adomian decomposition method is also employed to compute an approximation to the solution of the non linear system of differential equations governing the problem maple is used to carry out the computations graphical results are presented and discussed quantitatively to illustrate the solution

a new approach for the application of adomian decomposition method for the solution of fractional space diffusion equation with insulated ends abstract this paper presents the new approach for the solution of the space fractional diffusion equation defined in finite domain by adomian decomposition method adm a typical example of special interest with fractional space derivative of order 1 2 is considered in the present analysis and solved by adm after expressing the initial condition as fourier series the explicit solution of the space fractional diffusion equation has been presented in the closed form and then the numerical solution has been represented graphically the behaviour of adomian solutions and the effects of different values of are shown graphically

restarted adomian method for system of nonlinear volterra integral equations in this paper we generalize restarted adomian method as a new method based on standard adomian method for solving system of nonlinear volterra integral equations

approximate solutions for boundary value problems of time fractional wave equation in this article we implement relatively a new analytical technique the adomian decomposition method for solving the boundary value problems of time fractional wave equation the fractional derivative is described in the caputo sense the decomposition method is used to construct analytical approximate solutions of time fractional wave equation subject to specified boundary conditions the solutions are calculated in the form of a convergent series with easily computable components some examples are given the results reveal that the adomian method is very effective and convenient

a numerical solution of the coupled sine gordon equation using the modified decomposition method the modified decomposition method has been implemented for solving a coupled sine gordon equation we consider a system of coupled sine gordon equation which models one dimensional nonlinear wave processes in two component media by using an initial value system the numerical solutions of coupled sine gordon equation have been represented graphically

solving ratio dependent predator prey system with constant effort harvesting using adomian decomposition method abstract in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of the ratio dependent predator prey system with constant effort harvesting the convergence of the decomposition series is enhanced using pade approximation technique the qualitative analysis of the model reveals that constant effort prey harvesting may contribute to mutual extinction as a possible outcome of predator prey interaction some plots of the population of predator and prey versus time are presented to illustrate the performance and the accuracy of the algorithm the decomposition method has the advantage of being more concise for numerical purposes

analytical approximate solutions for nonlinear fractional differential equations we consider a class of nonlinear fractional differential equations fdes based on the caputo fractional derivative and by extending the application of the adomian decomposition method we derive an analytical solution in the form of a series with easily computable terms for linear equations the method gives exact solution and for non linear equations it provides an approximate solution with good accuracy several examples are discussed

comparison of the solutions obtained by adomian decomposition and wavelet galerkin methods of boundary value problems abstract in this paper we will compare the performance of adomian decomposition method and the wavelet galerkin method applied to the solution of boundary value problems involving non homogeneous heat and wave equations it is shown that the adomian decomposition method in many instances gives better results in the wavelet galerkin solutions daubechies six wavelets are used because they give better results than those of lower degree wavelets the results are then compared with those obtained using the adomian decomposition method although the adomian decomposition solution required slightly more computational effort than the wavelet galerkin solution it resulted in more accurate results than the wavelet galerkin method

numerical study of modified adomian s method applied to burgers equation the application of adomian s decomposition method to partial differential equations when the exact solution is not reached demands the use of truncated series but the solution s series may have small convergence radius and the truncated series may be inaccurate in many regions in order to enlarge the convergence domain of the truncated series pade approximants pas to the adomian s series solution have been tested and applied to partial and ordinary differential equations with good results in this paper pas both in x and t directions applied to the truncated series solution given by adomian s decomposition technique for burgers equation are tested numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution it is also shown in this paper that the application of adomian s method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences the so called method of lines may reduce the convergence domain of the solution s series

numerical computation of the nonlinear feedback operators for the nonquadratic time variant optimal control problems in this paper a reliable numerical algorithm for the nonlinear feedback operators for the time variant optimal control with nonquadratic criteria is constructed our approach rests mainly on the modified adomian decomposition method the convergence of the decomposition method as applied to the synthesis equations is investigated the proposed scheme avoids the complexity provided by using other techniques

an application of the modified decomposition method for two dimensional sine gordon equation in this study the decomposition method for solving two dimensional sine gordon equation has been implemented by using a number of initial values the explicit and numerical solutions of the equation are calculated the present method performs extremely well in terms of numerical accuracy and efficiency

non perturbative analytical solution of the general lotka volterra three species system the lotka volterra equations are solved for the general three species system using the adomian decomposition comparisons are shown for a prey predator model whose exact solution is available as well as for perturbative solution by murty and rao

on the numerical solution of the system of two dimensional burgers equations by the decomposition method adomian s decomposition method adm is proposed to approximate the numerical and analytical solutions of system two dimensional burgers equations stdbe with initial conditions the advantages of this work are the decomposition method reduces the computational work and improvement with regard to its accuracy and rapid convergence some examples are given to illustrate the performance of the method described

numerical study of lorenz s equation by the adomian method abstract in this paper we use the decomposition method of adomian for solving differential systems coming from physics meteorology we also give a comparison between the runge kutta method and the decomposition technique furthermore we reconfirm the famous butterfly effect

a numerical implementation of the decomposition method for the lienard equation in this study a kind of explicit exact and numerical solutions to the lienard equation is obtained and the applications of the results to this equation has been compared with their known theoretical solution this paper is particularly concerned with the adomian decomposition method and the numerical results demonstrate that the new method is relatively accurate and easily implemented

convenient analytic recurrence algorithms for the adomian polynomials abstract in this article we present four analytic recurrence algorithms for the multivariable adomian polynomials as special cases we deduce the four simplified results for the one variable adomian polynomials these algorithms are comprised of simple orderly and analytic recurrence formulas which do not require time intensive operations such as expanding regrouping parametrization and so on they are straightforward to implement in any symbolic software and are shown to be very efficient by our verification using mathematica 7 0 we emphasize that from the summation expressions a n k 1 n u n k for the multivariable adomian polynomials and an k 1 n f k u 0 c n k for the one variable adomian polynomials we obtain the recurrence formulas for the u n k and the c n k these provide a theoretical basis for developing new algorithmic approaches such as for parallel computing in particular the recurrence process of one particular algorithm for the one variable adomian polynomials does not involve the differentiation operation but significantly only the arithmetic operations of multiplication and addition are involved precisely c n 1 u n n 1 and c n k 1 n j 0 n k j 1 u j 1 c n 1 j k 1 2 k n we also discuss several other algorithms previously reported in the literature including the adomian rach recurrence algorithm 1 and this author s index recurrence algorithm 23 36