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

boundary effects in elasto plastic cosserat continua abstract the argument of discontinuous bifurcation is normally formulated for detecting spatial discontinuities in the interior of an infinite solution domain this paper expands localization analysis to a finite domain in which the translatory notion of classical continua is enriched by independent microrotations in the spirit of cosserat continua the bifurcation condition for the interior is augmented by complementing conditions at the boundaries and at material interfaces in analogy to the equivalent propagation argument for rayleigh surface waves and stoneley waves within the traditional format of elasto plasticity see needleman a and ortiz m 1991 effect of boundaries and interfaces on shear band localization int j solids struct 28 859 877 the current study develops the complementing propagation conditions for the micropolar cosserat description of elasto plasticity to this end their singularities are examined in terms of stationary rayleigh surface waves and stoneley waves at interior interfaces

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

classical and quantum integrability of a derivative nonlinear schrodinger model related to quantum group an ultralocal structure discovered in a derivative nonlinear schrodinger model enables us to investigate the complete integrability of the classical system through action angle variables and solve exactly the quantum model by quantum inverse scattering transformation exploiting the underlying quantum group related sklyanin like algebra an exact lattice version of the model is constructed and also the deep rooted reason for the existence of such an ultralocal model is revealed

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

solution of the system of ordinary differential equations by adomian decomposition method in this article we use adomian decomposition method which is a well known method for solving functional equations now a days to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one theoretical considerations are being discussed and convergence of the method for theses systems is addressed some examples are presented to show the ability of the method for linear and non linear systems of differential equations

the theoretical foundation of the adomian method abstract in this paper we work out the theoretical basis of the adomian method this powerful method that g adomian has developed in the beginning of the 1980 s supplies analytical approximations to the solution of many kinds of equations thanks to our decomposition theory we justify the practical method and we generalize the convergence results obtained by y cherruault afterward we explain how to solve rigorously equations with linear nonlinear or composed operator and also equations with several terms or with a second member

comparison between adomian s method and he s homotopy perturbation method in this paper it is revealed that modified form of he s homotopy perturbation method corresponds to adomian s decomposition method for certain nonlinear problems

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

an analytic approximation to the solution of heat equation by adomian decomposition method and restrictions of the method adomian decomposition has been applied to solve many functional equations so far in this article we have used this method to solve the heat equation which governs on numerous scientific and engineering experimentations some special cases of the equation are solved as examples to illustrate ability and reliability of the method restrictions on applying adomian decomposition method for these equations are discussed

localized failure analysis in elastoplastic cosserat continua this paper summarizes our experience with localized failure analysis in micropolar cosserat continua the main intent is to examine the regularization properties of discontinuous bifurcation problems when higher grade micropolar materials that exhibit an internal length scale are introduced thereby the key feature is the endowment of micropolar continua with rotational drilling degrees of freedom in addition to the traditional description of motion in terms of displacements after a brief review of elastoplastic cosserat continua we examine recent findings of localization analysis of discontinuous bifurcation 1 to this end we generalize the strength concept of the mohr envelope condition to non symmetric stress states to analyze the localization condition of discontinuous failure 2 the mohr representation of stress leads to a geometrical condition which is used to determine critical hardening softening moduli and localization directions that characterize the particular mode of failure this geometric interpretation of the localization condition lends itself to a systematic study of regularizing weak discontinuities within elastoplastic cosserat continua for illustration of these theoretical findings numerical failure studies are carried out on a representative volume element made of j2 type elastoplastic cosserat material the computational failure simulations demonstrate the non local character of cosserat continua that depends on an internal length scale and on the degree of non symmetry in the stress and strain states the computational results also illustrate the conversion of the underlying failure mode from mixed mode to mode i type failure of decohesion and separation

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

remark on modifications of adomian decomposition method a vital exception to the superiority of the chebyshev polynomial modification of the adomian decomposition method to other recent modifications is shown in this article also a new modification of the decomposition method is proposed and shown to be reliable

an approximation to the solution of hyperbolic equations by adomian decomposition method and comparison with characteristics method adomian decomposition method has been applied to solve many functional equations so far in this work this method is applied to solve hyperbolic partial differential equations and results will be compared with characteristics method

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

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube 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

new method for calculating adomian polynomials in this paper we introduce a new method for calculating adomian polynomials implementing the new method is very similar to using derivative operator which is familiar to everyone

recurrence triangle for adomian polynomials in this paper a recurrence technique for calculating adomian polynomials is proposed the convergence of the series for the adomian polynomials is discussed and the dependence of the convergent domain of the solution s decomposition series n 0 u n on the initial component function u 0 is illustrated by introducing the index vectors of the adomian polynomials the recurrence relations of the index vectors are discovered and the recurrence triangle is given the method simplifies the computation of the adomian polynomials in order to obtain a solution s decomposition series with larger domain of convergence we illustrate by examples that the domain of convergence can be changed by choosing a different u 0 and a modified iteration

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

solution of systems of integral differential equations by adomian decomposition method in this article adomian decomposition method as a well known method for solving functional equations has been employed to solve systems of integral differential equations theoretical considerations are discussed and convergence of the method for these systems is addressed some examples are presented to show the ability of the method for such systems

an improvement to an alternate algorithm for computing adomian polynomials in special cases in a published article entitled an alternate algorithm for computing adomian polynomials in special cases by the first author and some of his collaborators the algorithm were applied in special cases which restricts the application of the algorithm in this article new ideas are suggested for applying the algorithm in any cases without any more assumptions some examples are presented to illustrate the applications of the algorithm in more comprehensive situations and also to show the ability and simplicity of the algorithm

solution of wave equation by adomian decomposition method and the restrictions of the method adomian decomposition has been applied to solve many functional equations so far in this article we have used this method to solve the wave equation which governs numerous engineering experimentations particularly in geoscience applications some special cases of the equation are solved as examples to illustrate the reliableness of the method restrictions on using adomian decomposition method for these equations 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

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

a simple lattice version of the nonlinear schrodinger equation and its deformation with an exact quantum solution a lattice version of the quantum nonlinear schrodinger nls equation is considered which has a significant simple form and fulfils most of the criteria desirable for such lattice variants of field models unlike most of the known lattice nls equations the present model belongs to a class which does not exhibit the usual symmetry properties however this lack of symmetry itself seems to be responsible for the remarkable simplification of the relevant objects in the theory such as the lax operator the hamiltonian and other commuting conserved quantities as well as their spectra the model allows exact quantum solution through the algebraic bethe ansatz and also a straightforward and natural generalization to the vector case thus giving a new exact lattice version of the vector nls model a deformation representing a new quantum integrable system involving tamm dancoff like q boson operators is constructed

extension of the exp function method for systems of two dimensional burgers equations the exp function method has been applied to solve many functional equations so far but it has not been used for systems of equations directly in this paper the exp function method is applied to obtain generalized solitonary solutions of a system of two dimensional burgers equations stdbe it has been shown that the exp function method with the help of symbolic computation provides a very effective and powerful mathematical tool for solving a system of functional equations

solution of the epidemic model by adomian decomposition method in this article the problem of the spread of a non fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered mathematical modeling of the problem leads to a system of non linear ordinary differential equations adomian decomposition method is employed to solve this system of non linear ordinary differential equations the problem of convergence has been addressed

an alternate algorithm for computing adomian polynomials in special cases in this article we introduce an alternate algorithm for computing adomian polynomials and present some examples to show the simplicity and efficiency of the new method

finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects micropolar theories offer a possibility to model size effects in the constitutive behaviour of materials typical feature of such models is that they deal with a microrotation which is supposed to represent an independent state variable and its space gradient as a consequence the stress tensor is no longer symmetric and couple stresses enter the theory accordingly a micropolar plasticity law exhibiting kinematic hardening effects should account for both a back stress tensor and a back couple stress tensor this has been considered in the micropolar plasticity model developed by grammenoudis and tsakmakis the purpose of the current paper is to specify some constitutive functions in this model to elucidate the finite element implementation as well as to demonstrate its capabilities in describing size effects copyright 2005 john wiley sons ltd

the decomposition method for initial value problems abstract in this paper initial value problems for the heat wave and plate equations in which the vectorial space variable varies in the whole r d will be handled using the reliable decomposition method the solutions are obtained in the form of rapidly convergent power series with elegantly computable terms showing that the new technique is reliable powerful and promising

numerical solution of duffing equation by the laplace decomposition algorithm the laplace decomposition algorithm lda is a numerical algorithm can be adapted to solve duffing equations this paper both describes the principle of lda and discusses its advantages and drawbacks concrete example are also studied to show with numerical results how the lda works efficiently

algebraic approach in unifying quantum integrable models a novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given r matrix through reductions of an ancestor lax operator and its different realizations along with known discrete and field models a new class of inhomogeneous and impurity models is obtained

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

a new algorithm for the decomposition solution of nonlinear differential equations in this paper we introduce a new algorithm for applying the adomian decomposition method to nonlinear differential and partial differential equations the proposed algorithm does not require the explicit evaluation of adomian polynomials to approximate the nonlinearity term the numerical experiments show that the proposed algorithm is more accurate at larger values for time though at the cost of more computations

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

new series of integrable vertex models through a unifying approach applying a unifying lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed which exhibits a rich variety for generic q q roots of unity and q 1 exact solutions are formulated through an algebraic bethe ansatz and the novel possibility of hybrid vertex models is introduced

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

a computational method for solution of the prey and predator problem in this article a mathematical model of the problem of prey and predator being presented and adomian decomposition method is employed to compute an approximation to the solution of the system of nonlinear volterra differential equations governing on the problem some plots for the population of the prey and predator versus time are presented to illustrate the solution

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

new integrable quantum chains combining different kinds of spins a general procedure to generate new integrable hamiltonians combining to any kind of spins distributed arbitrarily on the line is given as a concrete application anisotropic chains formed by spin 1 2 and spin 1 operators at alternating sites are presented and solved exactly by the bethe ansatz ba the authors compute the ground state and excitation energies and momentum the higher order ba equations are derived depending on the choice these new hamiltonians exhibit or not conformal invariance in their low energy spectrum