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

first passage percolation network flows and electrical resistances we show that the first passage times of first passage percolation on 2 are such that p 0n n decay geometrically as n where may represent any of the four usual first passage time processes the former estimate requires no moment condition on the time coordinates but there exists a geometrically decaying estimate for the latter quantity if and only if the time coordinate distribution has finite moment generating function near the origin here is the time constant and 0 we study the line to line first passage times and describe applications to the maximum network flow through a randomly capacitated subsection of 2 and to the asymptotic behaviour of the electrical resistance of a subsection of 2 when the edges of the subsection are wires in an electrical network with random resistances in the latter case we show for example that if each edge resistance equals 1 or ohms with probabilities p and 1 p respectively then the effective resistance rn across opposite faces of an n by n box satisfies the following a if p 1 2 then p rn 1 as n b if p 1 2 then there exists p such that p p 1 underset raise0 3em hbox smash scriptscriptstyle leqslant mathop lim inf r n limits n to infty underset raise0 3em hbox smash scriptscriptstyle leqslant mathop lim sup r n limits n to infty underset raise0 3em hbox smash scriptscriptstyle leqslant v p 1

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

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

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

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

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

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

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

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

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

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 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

representations of non splittable extension algebras let a be an algebra over a field k and d a self duality d mod a 2 mod aop where aop is the opposite algebra of a and mod a the category of finitely generated left a modules by an extension for short we understand an extension algebra t over a with kernel da in the sense of cartan eilenberg 3 0 da t p a 0 where p is an algebra epimorphism in the case where a is hereditary by means of the heller function qaxda the auslander reiten quiver rawda of the trivial extension a k da is completely determined by ra lo moreover for any extension t tr is isomorphic to rawda it seems that this fact suggests the existence of a closer connection between some categories of modules over t and over a 1x da though mod t is not in general equivalent to mod a k da in this paper we are concerned with categorical relations between non splittable extensions and the trivial extensions and we shall establish some relation between them for some class of algebras to which hereditary algebras belong we prove the following where mod a denotes the category of finitely generated left a modules without projective summands

a reliable technique for solving the wave equation in an infinite one dimensional medium in this paper the initial value problem of the one dimensional wave equation where the domain of the space variable is unbounded will be handled by using the reliable decomposition method the solution is obtained in the form of a rapid convergent power series with elegantly computable terms comparing the decomposition method we used with several other methods that have been advanced for solving this model shows that the new technique is reliable powerful and promising

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

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

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

limit theorems for maximum flows on a lattice we independently assign a non negative value as a capacity for the quantity of flows per unit time with a distribution f to each edge on the mathbf z d lattice we consider the maximum flows through the edges from a source to a sink in a large cube in this paper we show that the ratio of the maximum flow and the size of the source is asymptotic to a constant this constant is denoted by the flow constant by the max flow and min cut theorem this is equivalent to a statement about the asymptotic behavior of the minimal value assigned to any surface on the large cube we can also show that there exists such a surface that is proportional to the size of the faces of the cube

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

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

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 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

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

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

cubic splines method for solving fourth order obstacle problems in this paper we develop a new cubic spline method for computing approximate solution of a system of fourth order boundary value problems associated with obstacle unilateral and contact problems it is shown that the present method is of order two and gives approximations which are better than those produced by some other collocation finite difference and spline methods numerical examples are presented to illustrate the applicability of the new method

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

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

quartic spline method for solving fourth order obstacle boundary value problems in this paper we use uniform quartic polynomial splines to develop a new method which is used for computing approximations to the solution and its first second as well as third derivatives for a system of fourth order boundary value problems associated with obstacle unilateral and contact problems it is shown that the present method is of order two and gives approximations which are better than those produced by other collocation and finite difference methods numerical examples are presented to illustrate the applicability of the new method

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

numerical methods for unilateral problems abstract the theory of variational inequalities besides being elegant and synthetic also provides a unified general framework for applying the numerical methods for solving many unrelated free boundary value problems in this paper we describe numerical experience on the use of variational inequalities and pade approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity like those describing the equilibrium configuration of an elastic beam stretched over an elastic obstacle in the case of a known obstacle these problems can be alternatively formulated as nonlinear boundary value problems without constraints for which the technique of pade approximants can be successfully employed the variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution

adaptive optimal control approximation for solving a fourth order elliptic variational inequality an optimal control approach is proposed to solve the fourth order elliptic variational inequality with curvature obstacle it is proved that the variational inequality is equivalent to the constrained optimal control problem the finite element approximation of the optimal control problem is constructed and the a priori error estimates and the equivalent a posteriori error estimators are derived some numerical experiments are performed to confirm a priori error estimates and demonstrate the effectiveness of the a posteriori estimators

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

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

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

on selfinjective algebras of finite representation type with maximal almost split sequences abstract we investigate the structure of finite dimensional selfinjective algebras of finite representation type over an arbitrary field having almost split sequences of modules whose middle term admits the maximal possible number of indecomposable direct summands

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 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

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

random growth models with polygonal shapes we consider discrete time random perturbations of monotone cellular automata ca in two dimensions under general conditions we prove the existence of half space velocities and then establish the validity of the wulff construction for asymptotic shapes arising from finite initial seeds such a shape converges to the polygonal invariant shape of the corresponding deterministic model as the perturbation decreases in many cases exact stability is observed that is for small perturbations the shapes of the deterministic and random processes agree exactly we give a complete characterization of such cases and show that they are prevalent among threshold growth ca with box neighborhood we also design a nontrivial family of ca in which the shape is exactly computable for all values of its probability parameter

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 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

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

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

nondifferentiability of the time constants of first passage percolation we study the paths of minimal cost for first passage percolation in two dimensions and obtain an exponential bound on the tail probability of the ratio of the lengths of the shortest and longest of these this inequality permits us to answer a long standing question of hammersley and welsh on the shift differentiability of the time constant specifically we show that for subcritical bernoulli percolation the time constant is not shift differentiable when p is close to one half

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

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

d representation finite self injective algebras abstract in this paper we initiate the study of higher dimensional auslander reiten theory of self injective algebras we give a systematic construction of weakly d representation finite self injective algebras as orbit algebras of the repetitive categories of algebras of finite global dimension satisfying a certain finiteness condition for the serre functor the condition holds in particular for all fractionally calabi yau algebras of global dimension at most d this generalizes riedtmann s classical construction of representation finite self injective algebras our method is based on an adaptation of gabriel s covering theory for k linear categories to the setting of higher dimensional auslander reiten theory applications include n fold trivial extensions and classical and higher preprojective algebras which are shown to be d representation finite in many cases we also get a complete classification of all d representation finite self injective nakayama algebras for arbitrary d

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

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

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

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

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

extensions over hereditary artinian rings with self dualities i in this paper we study the finitely generated indecomposable modules over an arbitrary extension over an artinian ring with self morita duality let a be an artinian ring with self duality and t an extension over a with kernel q see 11 chap xiv sect 21 such that qa and a q are isomorphic to injective hulls of top a and topla respectively such an a module q will be called quasi frobenius then it will be proved that