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

average rate of downlink heterogeneous cellular networks over generalized fading channels a stochastic geometry approach in this paper we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks the framework leverages recent application of stochastic geometry to other cell interference modeling and analysis the heterogeneous cellular network is modeled as the superposition of many tiers of base stations bss having different transmit power density path loss exponent fading parameters and distribution and unequal biasing for flexible tier association a long term averaged maximum biased received power tier association is considered the positions of the bss in each tier are modeled as points of an independent poisson point process ppp under these assumptions we introduce a new analytical methodology to evaluate the average rate which avoids the computation of the coverage probability pcov and needs only the moment generating function mgf of the aggregate interference at the probe mobile terminal the distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions including composite fading channels with small and mid scale fluctuations in addition our method can efficiently handle correlated log normal shadowing with little increase of the computational complexity the proposed mgf based approach needs the computation of either a single or a two fold numerical integral thus reducing the complexity of pcov based frameworks which require for general fading distributions the computation of a four fold integral

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

global existence of solutions for compressible navier stokes equations with vacuum abstract in this paper we will investigate the global existence of solutions for the one dimensional compressible navier stokes equations when the density is in contact with vacuum continuously more precisely the viscosity coefficient is assumed to be a power function of density i e a where a and are positive constants new global existence result is established for 0 1 when the initial density appears vacuum in the interior of the gas which is the novelty of the presentation

compressible navier stokes equations with degenerate viscosity coefficient and vacuum in this paper we consider the compressible navier stokes equations for isentropic flow of finite total mass when the initial density is either of compact or infinite support the viscosity coefficient is assumed to be a power function of the density so that the cauchy problem is well posed new global existence results are established when the density function connects to the vacuum states continuously for this some new a priori estimates are obtained to take care of the degeneracy of the viscosity coefficient at vacuum we will also give a non global existence theorem of regular solutions when the initial data are of compact support in eulerian coordinates which implies singularity forms at the interface separating the gas and vacuum

existence of solutions to a model for sparse one dimensional fluids abstract we prove the global existence of solutions to a model for a viscous compressible barotropic fluid initially occupying a general open subset of a finite one dimensional interval the fluid equations are applied only on the support of the density understood in the sense of distributions this support must be tracked and accommodation must be made for the possibly infinite number of collisions of fluid packets occurring on a possibly dense set of collision times our approach avoids certain nonphysical properties of solutions which are constructed as limits of solutions in which artificial mass has been inserted

super cubic iterative methods to solve systems of nonlinear equations two super cubic convergence methods to solve systems of nonlinear equations are presented the first method is based on the adomian decomposition method we state and prove a theorem which shows the cubic convergence for this method but numerical examples show super cubic convergence the second method is based on a quadrature formulae to obtain the inverse of jacobian matrix numerical examples show high order convergence for both methods

on the analytic solutions of the nonhomogeneous blasius problem in this article a totally analytic solution of the nonhomogeneous blasius problem is obtained using the homotopy analysis method ham this solution converges for 0 l c an analytical value of the critical value of l c was also obtained for the first time

a new analytic algorithm of lane emden type equations an reliable ease to use analytic algorithm is provided for lane emden type equation which models many phenomena in mathematical physics and astrophysics this algorithm logically contains the well known adomian decomposition method different from all other analytic techniques this algorithm itself provides us with a convenient way to adjust convergence regions even without pade technique some applications are given to show its validity

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

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

harmonic wave generation in non linear thermoelasticity by variational iteration method and adomian s method this paper applies the variational iteration method and adomian s decomposition method to solve numerically the harmonic wave generation in a nonlinear one dimensional elastic half space model subjected initially to a prescribed harmonic displacement the results show that the variational iteration method is much easier more convenient and more stable and efficient than adomian decomposition method

on the order of convergence of adomian method in this paper we contemplate the order of convergence of the decomposition method and we apply the results to some problems

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

compressible navier stokes equations with degenerate viscosity coefficient and vacuum ii abstract this is a continuation of the paper comm math phys 230 2002 329 on the study of the compressible navier stokes equations for isentropic flow when the initial density connects to vacuum continuously the degeneracy appears in the initial data and has effect on the viscosity coefficient because the coefficient is assumed to be a power function of the density this assumption comes from physical consideration and it also gives the well posedness of the cauchy problem a new global existence result is established by some new a priori estimates so that the interval for the power of the density in the viscosity coefficient is enlarged to 0 1 3

exact solutions to nonlinear schrodinger equation with variable coefficients abstract according to ma fuchsseiter s idea a trial equation method was proposed to find the exact envelop traveling wave solutions to some nonlinear differential equations with variable coefficients as an application combining with the complete discrimination system for polynomial some exact envelop traveling wave solutions to schrodinger equation with variable coefficients were obtained at the same time the physical meanings of the obtained solutions are discussed and the problem needed to further study is pointed out

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

gaussian class multivariate weibull distributions theory and applications in fading channels ascertaining on the suitability of the weibull distribution to model fading channels a theoretical framework for a class of multivariate weibull distributions originated from gaussian random processes is introduced and analyzed novel analytical expressions for the joint probability density function pdf moment generating function mgf and cumulative distribution function cdf are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers two specific distributions with arbitrary number of correlated variates are considered and studied with exponential and with constant correlation where their pdfs are introduced both cases assume equal average fading powers but not necessarily identical fading parameters for the multivariate weibull distribution with exponential correlation useful corresponding formulas as for the bivariate case are derived the presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection equal gain and maximal ratio combining mrc techniques operating over correlated weibull fading channels for these diversity receivers several useful performance criteria such as the moments of the output signal to noise ratio snr including average output snr and amount of fading and outage probability are analytically derived moreover the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach the proposed mathematical analysis is complemented by various evaluation results showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance

performance of digital linear modulations on weibull slow fading channels a closed form expression is derived for the moment generating function of the weibull distribution valid when its fading parameter assumes integer values expressions for average signal to noise ratio signal outage and average symbol error rate are derived for single channel reception and independent multichannel diversity reception operating on flat weibull slow fading channels

exact solutions to one dimensional non homogeneous parabolic problems by the homogeneous adomian decomposition method in this paper we propose a reliable modification of adomian decomposition method namely the homogeneous adomian decomposition method hadm that solves one dimensional non homogeneous parabolic equations with a variable coefficient the effectiveness of this method is verified through illustrative examples

an aftertreatment technique for improving the accuracy of adomian s decomposition method abstract adomian s decomposition method adm is a nonnumerical method which can be adapted for solving nonlinear ordinary differential equations in this paper the principle of the decomposition method is described and its advantages as well as drawbacks are discussed then an aftertreatment technique at is proposed which yields the analytic approximate solution with fast convergence rate and high accuracy through the application of pade approximation to the series solution derived from adm some concrete examples are also studied to show with numerical results how the at works efficiently

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

solution of nonlinear equations by modified adomian decomposition method in this paper we modify the standard adomian method for solution of the nonlinear equation f x 0 four examples are presented and compared using standard and modified adomian methods

exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method the purpose of this study is to introduce a modification of the homotopy perturbation method using laplace transform and pade approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations two test examples are given the coupled nonlinear system of burger equations and the coupled nonlinear system in one dimensional thermoelasticity the results obtained ensure that this modification is capable of solving a large number of nonlinear differential equations that have wide application in physics and engineering

ber analysis for spatial modulation in multicast mimo systems in this paper we investigate the bit error rate ber for multicast multiple input multiple output mimo systems employing spatial modulation sm and its variants called multicast sm type mimo systems in rayleigh fading channels the system ber here is derived by first attaining the ber of the worst receiver of each channel realization set and then averaging over all possible sets we first consider the uncorrelated channels by exploiting the system statistics a tight ber upper bound is proposed and the diversity is discussed for the systems we then perform the asymptotic analysis and show that the ber of the multicast sm type mimo system can be alternatively analyzed by analyzing the simple point to point sm type mimo system with weibull fading channels through this property a closed form asymptotic ber upper bound is provided and the impact of the receiver number on ber is analyzed subsequently our investigation is extended to correlated channels where all the receivers share the same correlation statistics the ber analysis is performed again through the framework similar to the uncorrelated case in the analysis the tight upper bound is derived and the effect of correlations is analyzed moreover we provide an explicit expression for the snr degradation caused by the receive correlation through the analysis finally simulations are exploited to evaluate the ber of the multicast sm type mimo systems and validate the analyses

analytical solution of a fractional diffusion equation by adomian decomposition method this paper presents an analytical solution of a fractional diffusion equation by adomian decomposition method by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

he s variational iteration method for fourth order parabolic equations he s variational iteration method is applied to fourth order parabolic partial differential equations with variable coefficients to illustrate the ability and reliability of the method some examples are given revealing its effectiveness and simplicity

diversity and multiplexing tradeoff in general fading channels the optimal tradeoff between diversity gain and multiplexing gain for multiple inputmultiple output mimo channels has been studied recently under the independent and identically distributed i i d rayleigh fading assumption in this correspondence this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions including different fading types nonidentical fading distributions spatial correlation and nonzero channel means our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance

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

on the weibull mgf a closed form expression is derived for the moment generating function of the weibull distribution when its shape parameter is a rational number

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

algebraic equations with exponential terms abstract the decomposition method is applied to algebraic equations containing exponential terms the n term approximation n is rapidly damped as n increases yielding an oscillating convergence of superior accuracy n 5 and n 9 for k 2

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

on optimal replacement repair policy for multi state deteriorating products under renewing free replacement warranty in this paper a replacement repair model is developed to study a renewing free replacement warranty rfrw for a class of multi state deteriorating repairable products after a replacement the product warranty is renewed two parameters affect the manufacturer s decision to minimally repair or replace a failed item the product deterioration level at the time of failure and the remaining warranty time we derive an optimal replacement repair policy to minimise the expected warranty servicing cost per item sold in the case of a product with two different working states we are able to explicitly find the optimal values of the replacement repair parameters using the adomian decomposition method in general for n 2 it is impossible to find the optimal parameter values analytically hence a computational procedure for finding these optimal values is proposed for more clarification numerical examples are also presented

numerical solution of differential equations in the deterministic limit of stochastic theory although the methodology of stochastic differential equations was developed to achieve statistical separability in the stochastic case the deterministic limit is investigated both as a verification of the theory and also for possible value as a deterministic technique

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

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

solution of physical problems by decomposition recent generalizations are discussed and results are presented for the theory and applications of the decomposition method application is made to the duffing equation with an error of 0 0001 in only four terms and less than 10 16 in thirteen terms of the decomposition series application is also made to a dissipative wave equation a matrix riccati equation and advection diffusion nonlinear transport

on the solution of algebraic equations by the decomposition method abstract the decomposition method g adomian stochastic systems academic press new york 1983 developed to solve nonlinear stochastic differential equations has recently been generalized to nonlinear and or stochastic partial differential equations systems of equations and delay equations and applied to diverse applications as pointed out previously see reference above the methodology is an operator method which can be used for nondifferential operators as well extension has also been made to algebraic equations involving real or complex coefficients this paper deals specifically with quadratic cubic and general higher order polynomial equations and negative or nonintegral powers and random algebraic equations further work on this general subject appears elsewhere g adomian stochastic systems ii academic press new york in press

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 review of the decomposition method and some recent results for nonlinear equations abstract the decomposition method can be an effective procedure for solution of nonlinear and or stochastic continous time dynamical systems without usual restrictive assumptions this paper is intended as a convenient tutorial review of the method 1

high accuracy implicit variable mesh methods for numerical study of special types of fourth order non linear parabolic equations in this paper we propose a new implicit high order two level finite difference method of o k 2 k h l h l 3 for the solution of special type of 1d fourth order non linear parabolic partial differential equation of the form u x x x x 2 u x x t u t t f x t u u x u x x u t u x x x u x t a 0 and hl 0 are the mesh sizes in time and space coordinates respectively the third order variable mesh methods proposed are based on only three spatial grid points xl xl 1 meaning that no fictitious points are required for incorporating the boundary conditions we discuss how our formulation is able to handle linear singular problem the proposed two level finite difference method is shown to be unconditionally stable for a model linear problem we applied the proposed methods to find the numerical solution of more complex fourth order non linear equations like second order benjamin ono equation and the good boussinesq equation it is evident from the numerical experiments that the numerical results agree well with the exact solutions hence demonstrating the efficiency of the methods derived

the failure on continuous dependence on initial data for the navier stokes equations of compressible flow it is shown that physical solutions of the navier stokes equations for one dimensional compressible flow need not depend continuously on their initial data at least when vacuum states are allowed specifically two fluid regions initially separated by a third region of very low density 6 are considered it is shown that as delta to 0 the unique solutions corresponding to delta 0 do not in fact converge to a physical solution but rather to a nonphysical weak solution in which the two fluids cannot collide independent of their initial velocities and whose separate momenta need not be conserved a particular consequence is that solutions of the cavity problem delta 0 are not unique

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

equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations abstract we consider the solution of partial differential equations for initial boundary conditions using the decomposition method the partial solutions obtained from the seperate equations for the highest ordered linear operator terms are shown to be identical when the boundary conditions are general and asymptotically equal when the boundary conditions in one independent variable are independet of other variables

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

a vacuum problem for the one dimensional compressible navier stokes equations with density dependent viscosity this paper is concerned with the free boundary problem for the one dimensional compressible navier stokes equations with density dependent viscosity a local in time existence result is established when the initial density is of compact support and connects to the vacuum continuously c 2002 elsevier science usa

blowup of smooth solutions to the compressible navier stokes equation with compact density we present a sufficient condition on the blowup of smooth solutions to the compressible navier stokes equations in arbitrary space dimensions with initial density of compact support as an immediate application it is shown that any smooth solutions to the compressible navier stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support and an upper bound which depends only on the initial data on the blowup time follows from our elementary analysis immediately another implication is that there is no global small decay in time or even bounded in the case that all the viscosity coefficients are positive smooth solutions to the compressible navier stokes equations for polytropic fluids no matter how small the initial data are as long as the initial density is of compact support this is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum the blowup of smooth solutions to the compressible euler system with initial density and velocity of compact support is a simple consequence of our argument 1998 john wiley sons inc

solving concrete examples by adomian method in this note we extend the adomian decomposition method to solve two concrete problems the population problem and a problem from polymer rheology

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

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

extracting a general iterative method from an adomian decomposition method and comparing it to the variational iteration method in this work a new form of adomian decomposition method adm is presented by this form a general iterative method can be achieved in which there is no need of calculating adomian polynomials also this general iterative method is compared with the adomian decomposition method and variational iteration method vim and its advantages are expressed

necessary conditions for the appearance of noise terms in decomposition solutions series in this paper the phenomena of the noise terms that appear in the components of the series solution introduced by adomian and rach 1 will be examined extensively the phenomena is useful in demonstrating a fast convergence of the exact solution however the condition set by adomian and rach 1 in that these noise terms appear for every nonhomogeneous equation is not always true and the nonhomogeneity condition is not sufficient another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases several differential and integral equations will be tested to confirm the newly developed condition

a convenient computational form for the adomian polynomials abstract recent important generalizations by g adomian stochastic systems academic press 1983 have extended the scope of his decomposition method for nonlinear stochastic operator equations see also iterative method inverse operator method symmetrized method or stochastic green s function method very considerably so that they are now applicable to differential partial differential delay and coupled equations which may be strongly nonlinear and or strongly stochastic or linear or deterministic as subcases thus for equations modeling physical problems solutions are obtained rapidly easily and accurately the methodology involves an analytic parametrization in which certain polynomials an dependent on the nonlinearity are derived this paper establishes simple symmetry rules which yield adomian s polynomials quickly to high orders

an extension of the decomposition method for solving nonlinear equations and its convergence in this paper we propose an extension of the decomposition method for solving nonlinear equations after a summary of adomian s decomposition method adm a new kind of decomposition strategy for nonlinear functions in nonlinear equations is proposed and a generalized decomposition method gdm for solving nonlinear equations is presented under a rather mild condition the convergence of the gdm is proved also some concrete examples are studied to illustrate with numerical results how powerful the gdm is finally some general remarks conclude this study

an algorithm for solving bond pricing problem the nonlinear bond pricing problem has been extensively studied in the literature since an analytical solution is not readily available we will seek to find an approximate solution we will present a decomposition method due to adomian and show how to obtain a reasonable numerical solution to the bond pricing problem

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

comments on the basto semiao calheiros root finding method abstract in the recent paper m basto v semiao f l calheiros a new iterative method to compute nonlinear equations appl math comput 173 2006 468 483 a new cubically convergent iterative method for solving nonlinear equations was proposed in this paper we give some comments that point to significant similarity of the proposed method to the classic euler chebyshev method and discuss the efficiency of the new method in a comparison procedure involving five other third order methods with similar structure five numerical examples four of them used in the cited paper showed that the convergence behavior of the new method is equal or worse than competitive tested methods some comments on iterative methods involving the third derivative are also exposed

nonlinear stochastic differential delay equations abstract the methods used by adomian and his co workers to solve linear and nonlinear stochastic differential equations will be demonstrated to be applicable to differential equations deterministic or stochastic involving delays constant time dependent or random

performance of dual maximal ratio combining diversity in nonidentical correlated weibull fading channels using pade spl acute approximation in this letter we evaluate the performance of the dual branch maximal ratio combining mrc diversity scheme in nonidentical correlated weibull fading channels with arbitrary parameters we first use the pade spl acute approximation pa to find closed form rational expressions for the moment generating function mgf of the output signal to noise ratio snr of the mrc receiver different performance measures such as the outage probability and the average symbol error rate for different linear modulations are then presented using the well known mgf approach furthermore the effect of the input snrs unbalancing the severity of fading and the degree of correlation on the system performance are also studied our results are validated by comparing them with computer simulations and we show that the pa technique is indeed a convenient tool for such performance evaluation studies

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 reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

an improvement to the fixed point iterative method the problem of convergence of the fixed point iterative method has been studied in this article the main object of this article is to improve the convergence so that the number of iterations is reduced to just few iterations a technique is presented to increase the order of convergence as much as desired to illustrate the ability of this technique some examples for which regular method needs many times of iterations are presented

a two step adomian decomposition method the adomian decomposition method adm is a nonnumerical method for solving a wide variety of functional equations and usually gets the solution in a series form in this paper we propose an efficient modification of adm namely two step adomian decomposition method tsadm that will facilitate the calculations we then conduct a comparative study between the tsadm and previous methods with the help of several illustrative examples the results obtained indicate that the tsadm is effective and promising

exact solutions for variable coefficients fourth order parabolic partial differential equations in higher dimensional spaces in this paper analytic solution of variable coefficient fourth order parabolic partial differential equation in two and three space variables are developed the calculations are accelerated by using the noise terms phenomenon for nonhomogeneous problems numerical examples are investigated to illustrate the pertinent features of the proposed algorithm

approximate analytic solutions for a two dimensional mathematicalmodel of a packed bed electrode using the adomian decomposition method in this paper we solve a system of second order partial differential equations with non standard boundary conditions this system of equations is a mathematical model that describes distributions of the overpotential and reactant concentration in a working packed bed electrode for an electrochemical reactor to ensure the existence and uniqueness of the solutions for this model we choose standard instead of non standard boundary conditions and obtain approximate analytic solutions in the form of a series that rapidly converges using the adomian decomposition method the method is easily implemented using the symbol operations of scientific computational software such as matlab

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

nonlinear stochastic dynamical systems in physical problems abstract a number of important equations of physics are shown to fit into the structure of a nonlinear stochastic differential equation which can then be solved by the decomposition method

new representations for the gaussian class multivariate weibull distribution with constant correlation and applications novel single integral representations for the multivariate probability density functions pdfs and cumulative distribution functions cdfs of the gaussian class weibull distribution are derived the solutions are expressed in terms of familiar mathematical functions which are available in common mathematical software the well known equal constant correlation model is considered a special linear transformation of independent gaussian random variables is used to generate correlated weibull random variables the advantage of the new representation is that only a single integral computation is needed to compute a n dimensional distribution the new representation of the cdf is used for the performance evaluation of a selection diversity combiner operating in equally correlated weibull fading channels the new pdf representation is also used for an analysis of the moments of the output signal to noise ratio of an equal gain diversity combiner operating in equally correlated weibull fading channels

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method