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

on the convergence region for decomposition solutions abstract the author s decomposition method using his a n polynomials for the nonlinearities has been shown to apply to wide classes of nonlinear or nonlinear stochastic operator equations providing a computable accurate solution which converges rapidly in computation the above is sufficient for a rapid test of convergence region

explicit solutions of nonlinear partial differential equations explicit solutions are calculated by the decomposition method for burger s equation for comparison with other existing procedures such as similarity reduction etc

optimal sequences for cdma under colored noise a schur saddle function property we consider direct sequence code division multiple access ds cdma modeling interference from users communicating with neighboring base stations by additive colored noise we consider two types of receiver structures first we consider the information theoretically optimal receiver and use the sum capacity of the channel as our performance measure second we consider the linear minimum mean square error lmmse receiver and use the signal to interference ratio sir of the estimate of the symbol transmitted as our performance measure our main result is a constructive characterization of the possible performance in both these scenarios a central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied we show that the sum capacity is a saddle function it is convex in the additive noise covariances and concave in the user received powers in the linear receiver case we show that the mini average power required to meet a set of target performance requirements of the users is a saddle function it is convex in the additive noise covariances and concave in the set of performance requirements

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

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

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

the adomian decomposition method for fuzzy system of linear equations in this paper the application of the adomian method for solving fuzzy system of linear equations fsle is considered for a fsle has been shown that the adomian decomposition method is equivalent to the jacobi iterative method appl math comput in press the algorithm is illustrated by solving some numerical examples

solution of nonlinear equations by an ancient chinese algorithm in this paper we re study an ancient chinese algorithm the ying buzu shu in about second century bc known as the rule of double false position in west after 1202 ad the method can powerfully applied to solve nonlinear equations some examples are given

numerical solutions of the laplace s equation abstract this paper uses the sinc methods to construct a solution of the laplace s equation using two solutions of the heat equation a numerical approximation is obtained with an exponential accuracy we also present a reliable algorithm of adomian decomposition method to construct a numerical solution of the laplace s equation in the form a rapidly convergence series and not at grid points numerical examples are given and comparisons are made to the sinc solution with the adomian decomposition method the comparison shows that the adomian decomposition method is efficient and easy to use

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

the homotopy analysis method for solving the fornberg whitham equation and comparison with adomian s decomposition method in this work an analytical technique namely the homotopy analysis method ham is applied to obtain an approximate analytical solution of the fornberg whitham equation a comparison is made between the ham results and the adomian s decomposition method adm and the homotopy perturbation method hpm the results reveal that ham is very simple and effective the ham contains the auxiliary parameter h which provides us with a simple way to adjust and control the convergence region of solution series

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

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

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

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

a simple risk adjusted exponentially weighted moving average in such contexts as medical monitoring there is a need for a simple procedure to estimate the level of a smoothly changing dynamic process while adjusting for risk factors associated with heterogeneous nonnormal observations standard methods exist for when the data are normal and simple methods have been developed for nonnormal data without covariates the dynamic generalized linear model dglm may be considered a standard for nonnormal data with covariates but perhaps one that is overcomplicated for many contexts we propose adapting the standard exponentially weighted moving average ewma to take into account the effect of risk factors by approximating the correct exponential family likelihood we derive a risk adjusted ewma ra ewma that is essentially a standard ewma applied to pseudo observations which are the original observations adjusted for differential risk the ra ewma can be expressed as a type of filter in which current estimate previous estimate discounted predictive error we

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

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