variational iteration method for solving multispecies lotka volterra equations this paper applies the variational iteration method to multispecies lotka volterra equations comparisons with the adomian decomposition and the fourth order runge kutta methods show that the variational iteration method is a powerful method for nonlinear equations

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

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

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

hamiltonian path embedding and pancyclicity on the mobius cube with faulty nodes and faulty edges a graph g v e is said to be pancyclic if it contains fault free cycles of all lengths from 4 to v in g let f sub v and f sub e be the sets of faulty nodes and faulty edges of an n dimensional mobius cube mq sub n respectively and let f f sub v spl cup f sub e a faulty graph is pancyclic if it contains fault free cycles of all lengths from 4 to v f sub v in this paper we show that mq sub n f contains a fault free hamiltonian path when f spl les n 1 and n spl ges 1 we also show that mq sub n f is pancyclic when f spl les n 2 and n spl ges 2 since mq sub n is regular of degree n both results are optimal in the worst case

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

a mechanical algorithm for solving ordinary differential equation in this paper by using the theories and methods of mathematics analysis ordinary differential equation and computer algebra a reliable algorithm for solving ordinary differential equation ode was established and a new maple procedure mechodeproc was established too the results of the examples indicated that the procedure mechodeproc based on taylor polynomial method was simple and effective and could provide an accuracy approximate solution or exact solution of the ordinary differential equation this would be useful for solving differential equation

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

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

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

conditional edge fault tolerant edge bipancyclicity of hypercubes the hypercube has been one of the most popular interconnection networks for parallel computer communication systems in this paper we assume that each node is incident with at least two fault free links under this assumption we show that every fault free edge lies on a fault free cycle of every even length from 6 to 2 n inclusive even if it has up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated

a maple package of new adm pade approximate solution for nonlinear problems abstract based on the new definition of four classes of adomian polynomials proposed by rach in 2008 a maple package of new adomian pade approximate solution for solving nonlinear problems is presented this package combines the merits of the adomian decomposition method and the diagonal pade technique and may give more accurate solutions of nonlinear problems with strong nonlinearity besides the package is user friendly and efficient one only needs to input the initial conditions governing equation and four optional parameters then our package will output the analytic approximate solution within a few seconds where the equation is decomposed into three parts they are the linear term r nonlinear term nn and source function g which are all in functional form meanwhile several graphs generated from the above solutions are displayed and demonstrate a favorable comparison in this paper several different types of examples are given to illustrate the validity and promising flexibility of the package this package provides us with a convenient and useful tool for dealing with nonlinear problems as well as its electronic version is free to download via the journal website

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

the decomposition method applied to systems of partial differential equations and to the reaction diffusion brusselator model in this work systems of linear and nonlinear partial differential equations and the reaction diffusion brusselator model are handled by applying the decomposition method the advantage of this work is twofold firstly the decomposition method reduces the computational work secondly in comparison with existing techniques the decomposition method is an improvement with regard to its accuracy and rapid convergence the decomposition method has the advantage of being more concise for analytical and numerical purposes

classroom note numerical and analytical solutions of volterra s population model to illustrate various mathematical methods which may be used to solve problems of engineering mathematical physics and mathematical biology volterra s model for population growth of a species in a closed system is solved using several methods familiar to junior or senior level students in applied mathematics volterra s model is a first order integro ordinary differential equation where the integral term represents the effect of toxin accumulation on the species the solution methods used are i numerical methods for solving a first order initial value problem supplemented with numerical integration ii numerical methods for solving a coupled system of two first order initial value problems and iii phase plane analysis a singular perturbation solution previously presented is also outlined while conclusions drawn using the four methods are correlated the student may analyze and solve the problem using any of the methods independently of the others

an algorithm for solving the high order nonlinear volterra fredholm integro differential equation with mechanization abstract in this paper by using the theories and methods of mathematics analysis and computer algebra a reliable algorithm for solving high order nonlinear volterra fredholm integro differential equations was established and a new maple procedure voltfredproc was established too the results of the examples indicated that the procedure voltfredproc of taylor polynomial method is simple and effective and could provide an accuracy approximate solution or exact solution of the high order nonlinear volterra fredholm integro differential equation this would be useful for solving integro differential equation integral equations and ordinary differential equation

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

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

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

an algorithm for solving nonlinear singular perturbation problems with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving nonlinear singular perturbation problems was established a new maple procedure spp was established too the procedure spp give not only the approximate analytic solutions but also the numerical solutions of spp six examples are presented to illustrate the implementation of the program the method is very simple and effective for most of singular perturbation problems this would be useful for solving differential equations

pancyclicity and bipancyclicity of conditional faulty folded hypercubes a graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order the pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network s topology can simulate rings of various lengths an n dimensional folded hypercube fq n is an attractive variant of an n dimensional hypercube q n that is obtained by establishing some extra edges between the vertices of q n fq n for any odd n is known to be bipartite in this paper we explore the pancyclicity and bipancyclicity of fq n for any fq n n 2 with at most 2n 3 faulty edges where each vertex is incident to at least two fault free edges we prove that there exists a fault free cycle of every even length from 4 to 2 n and when n 2 is even we prove there also exists a fault free cycle of every odd length from n 1 to 2 n 1 the result is optimal with respect to the number of faulty edges tolerated

multiple regular graph embeddings into a hypercube with unbounded expansion as topological structures interconnection networks play an important role in parallel and distributed computer systems particularly in multicomputer systems which provide an effective mechanism for exchanging data between processors in this paper we study the node fault tolerant capability of an n dimensional hypercube with respect to multiple regular graph embeddings into a hypercube with unbounded expansion we present a fault tolerant method for multiple regular graph embeddings into a hypercube with dilation 3 congestion 1 and load 1 these results show that o n email protected log email protected 2 faults can be tolerated where n is the number of dimensions in a hypercube and l is the number of the nodes of the regular graph the presented embedding methods are mainly optimized for balancing the processor loads while minimizing load and congestion as far as possible furthermore our method expands on some previously known findings also this technology can be applied in grid computing and cloud computing

chord arc surfaces with small constant i abstract we introduce a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for curves in the plane we give various equivalent operator theoretic function theoretic and geometrical characterizations of these surfaces we not know any nice potential theoretic characterizations in a companion paper we address the issue of finding good parameterizations for these surfaces

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

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

normal cycles and curvature measures of sets with d c boundary abstract we show that for every compact domain in a euclidean space with d c delta convex boundary there exists a unique legendrian cycle such that the associated curvature measures fulfill a local version of the gauss bonnet formula this was known in dimensions two and three and was open in higher dimensions in fact we show this property for a larger class of sets including also lower dimensional sets we also describe the local index function of the legendrian cycles and we show that the associated curvature measures fulfill the crofton formula

stably embedded surfaces of bounded integral curvature we study the effect of simultaneous bounds on the local l1 norms of the second fundamental form and of the gauss curvature on the geometry of surfaces embedded in a riemannian manifold m such bounds are natural since together with an area bound they amount to a local bound on the area of the manifold of unit normals to living in the sphere bundle of m the main technical point is that given a sequence of surfaces i with uniform local bounds of this type converging in the hausdorff metric topology to a surface 0 the length space structures of the i converge to that of 0 i e distances do not collapse it follows that under suitable local topological conditions the surface 0 is a manifold of bounded integral curvature mbc in the sense of alexandrov under all smooth complete changes of the metric on m in particular the boundary of a convex set with nonempty interior in any smooth complete m3 is mbc our method is to construct local coordinates for smoothly embedded surfaces satisfying w1 bv bounds based solely on curvature integrals in the process we demonstrate a regularity property for cut loci of surfaces

a modified adomian method for system of nonlinear differential equations in this paper a modified adomian method is introduced to solve some systems of nonlinear differential equations the method can be mechanized in maple and a procedure is written to solve the approximate analytic solution of the systems some examples will be presented to illustrate the effectiveness of the method and the procedure a comparison between the program and the original adomian method s program is drawn

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

the numerical solution of sixth order boundary value problems by the modified decomposition method a fast and accurate algorithm is developed for the solution of sixth order boundary value problems bvps with two point boundary conditions a modified form of the adomian decomposition method is applied to construct the numerical solution for such problems the scheme is tested on one linear and two nonlinear problems the results demonstrate reliability and efficiency of the algorithm developed

a comparison between adomian decomposition method and taylor series method in the series solutions in this work we will compare the performance of the adomian decomposition method and the taylor series method applied to the solution of linear and nonlinear ordinary differential equations the comparison shows that the decomposition method is reliable efficient and easy to use from a computational viewpoint although the two methods provide the solution in an infinite series the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by taylor series method

a new mechanical algorithm for solving the second kind of fredholm integral equation integral equation has been one of principal tool of various areas of applied mathematics physics and engineering in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of fredholm integral equation is established and a mechanical maple algorithm fredholmproc is established too the algorithm can provide the continuous solution of the second kind of fredholm integral equation ten examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for solving the integral equation

the spanning laceability on the faulty bipartite hypercube like networks a w container c u v of a graph g is a set of w disjoint paths joining u to v a w container of g is a w container if it contains all the nodes of v g a bipartite graph g is w laceable if there exists a w container between any two nodes from different parts of g let n and k be any two positive integers with n 2 and k

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

a new approach to the electrostatic pull in instability of nanocantilever actuators using the adm pade technique in this paper the adomian decomposition method and pade approximants are integrated to study the deflection and pull in instability of nanocantilever electromechanical switches in a distributed parameter model intermolecular forces including casimir forces are taken into account considering their range of application a closed form power series solution based on adomian polynomials is obtained the obtained analytic results are compared with numerical solution the adomian method is accurate for small deflections but the results of a pull in instability study demonstrate that the accuracy of the adomian solution is not as good for small deflections thus to increase the accuracy of the adomian solution for the pull in instability the adomian power series is converted to pade approximants the results of the present method are compared with the numerical results as well as those of the adomian decomposition method and other methods reported in the literature the results obtained using the adm pade are remarkably accurate compared with the numerical results the proposed technique can be easily extended to solve a wide range of instability problems finally the minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular attractions which is an important parameter for the pull in instability of a nanocantilever actuator are calculated using adomian pade approximants

regular connected bipancyclic spanning subgraphs of hypercubes an n dimensional hypercube q n is a hamiltonian graph in other words q n n 2 contains a spanning subgraph which is 2 regular and 2 connected in this paper we explore yet another strong property of hypercubes we prove that for any integer k with email protected email protected n q n n 3 contains a spanning subgraph which is k regular k connected and bipancyclic we also obtain the result that every mesh p mxp n m n 2 is bipancyclic which is used to prove the property above

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

a mechanical algorithm for solving the volterra integral equation in this paper by using the theories and methods of integral equation and computer algebra a reliable algorithm for solving the volterra integral equation is established and a new maple algorithm mainproc is established too some examples are presented to illustrate the implementations of the algorithm the results of the examples indicate that the algorithm of taylor polynomial method is simple and effective and can provide an accuracy approximate solution or exact solution of the volterra integral equation and integro differential equation this will be useful for solving a system of integral equation or integro differential equation

mechanization for solving spp by reducing order method in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of reduction of order approximation method for solving singular perturbation problems was established a new maple procedure redordproc was established too the procedure redordproc give not only the approximate analytic solutions but also the numerical solutions of the kinetics problems some examples are presented to illustrate the implementation of the program

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

mechanical algorithm for solving the second kind of volterra integral equation in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of volterra integral equation is established and a new maple procedure voltproc is established too in particular the algorithm can provide the exact solution of the second kind of volterra integral equation by the methods of neumann series and mathematical induction i e the algorithm also can computing the nth term by finite terms of the iterative kernel some examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for the integral equation solving and mathematical theorems automatic proving

computations of multi resultant with mechanization abstract resultant is a classical algebraic tool for determining whether or not a polynomial systems have a common root without explicitly solving for the roots but the complexity of resultants can be very high in practice in this paper by using the theories and methods of computer algebra two reliable algorithms for computing multi resultant problems dixon resultant and macaulay resultant were established two new maple procedures dixonres and macaulayres were established too some examples are presented to illustrate the implementations of the programs this would be useful for solving a system of polynomial equations

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

linear array and ring embeddings in conditional faulty hypercubes the n dimensional hypercube qn is a graph having 2n vertices labeled from 0 to 2n 1 two vertices are connected by an edge if their binary labels differ in exactly one bit position in this paper we consider the faulty hypercube qn with n 3 that each vertex of qn is incident to at least two nonfaulty edges based on this requirement we prove that qn contains a hamiltonian path joining any two different colored vertices even if it has up to 2n 5 edge faults moreover we show that there exists a path of length 2n 2 between any two the same colored vertices in this faulty qn furthermore we also prove that the faulty qn still contains a cycle of every even length from 4 to 2n inclusive

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

conditional edge fault hamiltonicity of augmented cubes the augmented cube is a variation of hypercubes it possesses many superior properties in this paper we show that for any n dimensional augmented cube n 3 with faulty edges up to 4n 8 in which each vertex is incident to at least two fault free edges there exists a fault free hamiltonian cycle our result is optimal with respect to the number of faulty edges tolerated

new ideas for decomposing nonlinearities in differential equations abstract in this paper we consider the decomposition for the nonlinearity in a differential equation for the solution by decomposition by analyzing and transforming the taylor expansion of the nonlinearity about the initial solution component the decomposition of the nonlinearity is converted to the partitions of the solution sets for a class of diophantine equations this conversion simplifies the discussion and presents a new idea for decompositions we enumerate five types of partitions and their corresponding decomposition polynomials each of the last four types contains infinitely many kinds of decomposition polynomials in the form of finite sums in types 2 3 and 4 there is a parameter q and each value of q corresponds to a class of decomposition polynomials in type 5 each positive integer sequence c j satisfying 1 c 1 c 2 and j c j for j 2 3 corresponds to a class of decomposition polynomials four classes of the adomian polynomials r rach a new definition of the adomian polynomials kybernetes 37 2008 910 955 are derived as particular cases

approximate analytical solutions for a mathematical model of a tubular packed bed catalytic reactor using an adomian decomposition method abstract in this paper a mathematical model of a tubular packed bed catalytic reactor which is modeled by a system of strongly nonlinear second order partial differential equations with incompatible boundary conditions will be solved by properly using the boundary conditions and correctly choosing the solution search direction approximate analytic solutions for the model can be obtained by the adomian decomposition method when the values of the dimensionless parameters in the system are assigned within a suitable range the solutions describe objectively the distributions of the temperature and key reactant concentration in the reactor

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