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

numerically solution of fuzzy differential equations by adomian method in this paper a method for numerical approximation of fuzzy first order initial value problem is presented buckly and feruing fuzzy sets syst 110 2000 43 have solved fuzzy first order initial value problem they solved problem in crisp case and then extend the solution to fuzzy case in this paper we use adomian method to find the approximate solution in crisp case and extend it to fuzzy case using this method we solve problems that the classical methods could not be applied for them in crisp case

a representation theorem for cyclic analytic two isometries a bounded linear operator t on a complex separable hilbert space z is called a 2 isometry if t 2t2 2t t i o we say that t is analytic if nn 0 tnt 0 in this paper we show that every cyclic analytic 2 isometry can be represented as multiplication by z on a dirichlet type space d 8 here ze denotes a finite positive borel measure on the unit circle for two measures u and v the 2 isometries obtained as multiplication by z on d 8 and d v are unitarily equivalent if and only if u v we also investigate similarity and quasisimilarity of these 2 isometries and we apply our results to the invariant subspaces of the dirichlet shift

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

nonperturbative approximate solution for lane emden equation a nonperturbative approximate analytical solution is derived for the lane emden equation using the adomian decomposition method the solution is in the form of a power series with easily computable coefficients the pade approximants method is used to accelerate the convergence of the power series comparison with some known exact and numerical solutions shows that the present solution is highly accurate

numerical method for solving fractional coupled burgers equations in this paper we use the fractional variational iteration method fvim to solve a time and space fractional coupled burgers equations some numerical examples are presented to show the efficiency of considered method a comparison of the proposed method is made with the exact solution adomain decomposition method adm generalized differential transformation method gdtm and homotopy perturbation method hpm

aspects of nonnormality for iterative methods abstract recently new optimal krylov subspace methods have been discovered for normal matrices in light of this novel ways to quantify nonnormality are considered in connection with various families of matrices we use as a criterion how for a given matrix these iterative methods introduced can be employed via e g inexpensive matrix factorizations the unitary orbit of the set of binormal matrices provides a natural extension of normal matrices its elements yield polynomially normal matrices of moderate degree in this context several matrix nearness problems arise

comparison of the solutions obtained by b spline fem and adm of kdv equation a numerical solution to a generalized korteweg de vries kdv equation is obtained using the galerkin method with quadratic b spline finite element method fem over which the nonlinear term is locally linearized and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

m isometric operators and their local properties abstract in this paper we give necessary and sufficient conditions for a bounded linear hilbert space operator to be an m isometry for an unspecified m written in terms of conditions that are applied to one vector at a time we provide criteria for orthogonality of generalized eigenvectors of an a priori unbounded linear operator t on an inner product space that correspond to distinct eigenvalues of modulus 1 we also discuss a similar question of when jordan blocks of t corresponding to distinct eigenvalues of modulus 1 are orthogonal

iterative methods improving newton s method by the decomposition method in this paper we present a sequence of iterative methods improving newton s method for solving nonlinear equations the adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses the orders of convergence are derived analytically and then rederived by applying symbolic computation of maple some numerical illustrations are given

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

on higher order selfadjoint operators abstract for a positive integer m and a hilbert space h an operator t in b h the space of all bounded linear operators on h is called m selfadjoint if k 0 m 1 k m k t k t m k 0 in this paper we show that if t b h and the spectrum of t consists of a finite number of points then it is m selfadjoint if and only if it is an n jordan operator for some integer n moreover we prove that if t is m selfadjoint then t is nilpotent when it is quasinilpotent then we characterize m selfadjoint weighted shift operators also we show that if t is m selfadjoint then so is p t when p z is a polynomial with real coefficients after that we investigate an elementary operator and a generalized derivation operator on the hilbert schmidt class c 2 h which are m selfadjoint finally we prove that no m selfadjoint operator on an infinite dimensional hilbert space can be n supercyclic for any n 1

a generalization of darbo s theorem with application to the solvability of systems of integral equations in this paper we give an extension of darbo s fixed point theorem associated with measures of noncompactness and present some results on the existence of coupled fixed points for a class of condensing operators in banach spaces moreover as an application we study the problem of existence of solutions for a general system of nonlinear integral equations

decomposing algebraic m isometric tuples abstract we show that any m isometric tuple of commuting algebraic operators on a hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple our approach applies as well to tuples of algebraic operators that are hereditary roots of polynomials in several variables

real linear kronecker product operations the kronecker product in the real linear matrix analytic setting is studied more versatile operations are proposed such generalizations are of interest for the same reasons the standard kronecker product is to give an example new preconditioning ideas are suggested in connection with this several formulae for the inverse are devised orthogonal decompositions of real entried matrices are derived through introducing new kronecker product svds matrix equations are given to illustrate how the kronecker product structures introduced can arise

identifying a control function in parabolic partial differential equations from overspecified boundary data determination of an unknown time dependent function in parabolic partial differential equations plays a very important role in many branches of science and engineering in the current investigation the adomian decomposition method is used for finding a control parameter p t in the quasilinear parabolic equation u t u x x p t email protected in 0 1 x 0 t with known initial and boundary conditions and subject to an additional condition in the form of 0 1k x u x t dx e t email protected email protected t which is called the boundary integral overspecification the main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known adomian decomposition method the decomposition procedure of adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form furthermore due to the rapid convergence of adomian s method a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution this method provides a reliable algorithm that requires less work if compared with the traditional techniques some illustrative examples are presented to show the efficiency of the presented method

a m isometries on hilbert spaces abstract a bounded linear operator t on a hilbert space h is called an a m isometry for some positive operator a on h and integer m if k 0 m 1 m k m k t k a t k 0 we give some properties of a m isometries in particular we focus on spectral properties and the relation between a m isometries and m isometries also we obtain some dynamic properties of a m isometries as a negative answer to 22 question 1 with an example of an a isometric which is n supercyclic and sufficient conditions for an a m isometry to be not n supercyclic moreover we prove that the perturbation of a m isometry by a bigger class than nilpotent operators is not n supercyclic

elementary properties of isometries on a hilbert space inspired by recent works on m isometries for a positive integer m in this paper we introduce the classes of isometries and unitaries on a hilbert space we show that an isometry on a finite dimensional complex hilbert space h with dimension n is in fact an 2n 1 isometry we describe the spectra of such operators study the quasinilpotent perturbations of isometries and characterize when tensor products of isometries are also isometries as a surprising by product we obtain a generalization of nagy foias langer decomposition of a contraction into an unitary and a completely nonunitary contraction

numerical methods for fourth order fractional integro differential equations this paper outlines a reliable strategy for solving linear and nonlinear boundary value problems for fourth order fractional integro differential equations the fractional derivative is considered in the caputo sense the adomian decomposition method is found to be fast and accurate numerical examples are presented to illustrate the efficiency and reliability of the method

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

an explicit and numerical solutions of some fifth order kdv equation by decomposition method in this paper by considering the adomian decomposition method explicit and numerical solutions are calculated for a various fifth order korteweg de vries equations with initial condition the method does not need linearization or weak nonlinearity assumptions perturbation theory the decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self canceling noise terms where sum of components vanishes in the limit

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

existence of solutions for a class of system of functional integral equation via measure of noncompactness abstract in this paper we give some generalization of darbo s fixed point theorem related to the measure of noncompactness and present some results on the existence of coupled fixed point theorem for a special class of operators in a banach space our results generalize and extend some comparable results in the literature also as an application we study the existence of solution for a class of the system of nonlinear functional integral equations finally an example illustrating the mentioned applicability is also included

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

existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness the aim of this paper is to establish fixed point theorems for condensing operators in the frechet spaces in our considerations we apply the technique of measures of noncompactness in conjunction with the tychonoff fixed point theorem moreover as an application we study the problem of the existence of solutions for infinite systems of integral equations in two variables the results obtained extend several ones finally an example is presented to show the efficiency of our results

an isometry plus a nilpotent operator is an m isometry applications abstract we prove that if an isometry a and a nilpotent operator q of order n commute then a q is a strict 2 n 1 isometry as an application of the main result we prove that a q cannot be n supercyclic for any n also we find an m isometry with prescribed spectrum k where k is the closed unit disk or a compact subset of the unit circle

solving ratio dependent predator prey system with constant effort harvesting using adomian decomposition method abstract in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of the ratio dependent predator prey system with constant effort harvesting the convergence of the decomposition series is enhanced using pade approximation technique the qualitative analysis of the model reveals that constant effort prey harvesting may contribute to mutual extinction as a possible outcome of predator prey interaction some plots of the population of predator and prey versus time are presented to illustrate the performance and the accuracy of the algorithm the decomposition method has the advantage of being more concise for numerical purposes

homotopy perturbation method for fractional fornberg whitham equation this article presents the approximate analytical solutions to solve the nonlinear fornberg whitham equation with fractional time derivative by using initial values the explicit solutions of the equations are solved by using a reliable algorithm like homotopy perturbation method the fractional derivatives are taken in the caputo sense numerical results show that the hpm is easy to implement and accurate when applied to time fractional pdes

classification of hereditary matrices abstract a classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices t such that p t 0 we consider matrices and operators which satisfy a different type of polynomial constraint let h be a complex hilbert space t be a bounded linear transformation of h t be the adjoint of t and c x y be the algebra of polynomials in x and y with complex coefficients for a polynomial p c x y in two variables with complex coefficients define p t m n 0 p m n t n t m where p m n is the coefficient of ynxm in the expansion of p in a power series about the point 0 0 t is called a root of p if and only if p t 0 note that if p c x y is a polynomial in the single variable x then the definition of p t given here agrees with the classical definition in this paper we study the relationships which p t 0 forces between p and t when t is an algebraic operator i e there exists n 1 and complex numbers a0 an 1 such that 0 a0 a1t an 1tn 1 tn the classification starts with the following observation suppose p c x y and an algebraic operator t l h satisfy p t 0 then certain subspaces of h which are invariant for t must be orthogonal or certain coefficients of p must vanish this leads to the notions of a graph attached to each p c x y and a graph attached to each square matrix t for diagonalizable t a necessary and sufficient graph theoretic condition for solving p t 0 is given for nondiagonalizable t this condition is necessary but not sufficient the use of these graphs does however reduce the problem to the problem of solving the equation p t 0 for t with exactly one or two eigenvalues for t with one eigenvalue we give a necessary and sufficient condition for solving p t 0 this leaves the case of solving p t 0 when t has exactly two eigenvalues this problem mixes algebra involving polynomials with matrix theory we show that it is equivalent to the purely algebraic problem of determining if equations of the form i j eci jxi r j s 0 have solutions of finite support with certain nonvanishing properties we call these equations bi hankel equations subordinate to a given subset e of the lattice of integer pairs i j 0 i m 1 0 j n 1 it turns out that there is an algorithm which uses grobner bases for determining if the type of solution we seek exists and for computing it

algebraic properties of operator roots of polynomials abstract properties of m selfadjoint and m isometric operators have been investigated by several researchers particularly interesting to us are algebraic properties of nilpotent perturbations of such operators mccullough and rodman showed in the nineties that if q n 0 and a is a selfadjoint operator commuting with q then the sum a q is a 2 n 1 selfadjoint operator very recently bermudez martinon and noda proved a similar result for nilpotent perturbations of isometries via a new approach we obtain simple proofs of these results and other generalizations to operator roots of polynomials

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

analytical approximate solutions for nonlinear fractional differential equations we consider a class of nonlinear fractional differential equations fdes based on the caputo fractional derivative and by extending the application of the adomian decomposition method we derive an analytical solution in the form of a series with easily computable terms for linear equations the method gives exact solution and for non linear equations it provides an approximate solution with good accuracy several examples are discussed

some results on higher order isometries and symmetries products and sums with a nilpotent operator abstract we study the sum of an m isometry or an m symmetric operator with a nilpotent operator we also study the product of two m isometries or two n symmetries we obtain several theorems generalizing previous work our method is straightforward and thus offers direct and simple insights into why these theorems are true

series solution to the pochhammer chreeequation and comparison with exact solutions in this study a decomposition method for approximating the solution of the pochhammer chreeequation is implemented by using this scheme explicit exact solution is calculated in the form of a convergent power series with easily computable components to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solutions known for some special cases

the decomposition method for ordinary differential equations with discontinuities in this paper the decomposition method is applied to the initial value problem ivp for ordinary differential equations with discontinuities for both linear and nonlinear cases

solving the problem of biological species living together by adomian decomposition method in this paper we use adomian decomposition method for solving the system of nonlinear integro differential equations derived from considering biological species living together

comparison of the solutions obtained by adomian decomposition and wavelet galerkin methods of boundary value problems abstract in this paper we will compare the performance of adomian decomposition method and the wavelet galerkin method applied to the solution of boundary value problems involving non homogeneous heat and wave equations it is shown that the adomian decomposition method in many instances gives better results in the wavelet galerkin solutions daubechies six wavelets are used because they give better results than those of lower degree wavelets the results are then compared with those obtained using the adomian decomposition method although the adomian decomposition solution required slightly more computational effort than the wavelet galerkin solution it resulted in more accurate results than the wavelet galerkin method

solving a multi order fractional differential equation using adomian decomposition abstract an algorithm has been developed to convert the multi order fractional differential equation d y t f t y t d 1 y t d n y t y k 0 c k k 0 m where m d denotes caputo fractional derivative of order into a system of fractional differential equations further adomian decomposition method has been employed to solve the system of fractional differential equations some illustrative examples are presented

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

application of modified decomposition method for the analytical solution of space fractional diffusion equation abstract spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow finance and others areas of application this paper presents the analytical solutions of the space fractional diffusion equations by modified decomposition method mdm by using initial conditions the explicit solutions of the equations have been presented in the closed form the decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self cancelling noise phenomenon two examples the first one is one dimensional and the second one is two dimensional fractional diffusion equation are presented to show the application of the present technique the present method performs extremely well in terms of efficiency and simplicity

elementary operators which are m isometries abstract the study of m isometry elementary operator of length one is initiated by botelho and jamison several authors have contributed to obtain this result if the two operator coefficients involved are m isometries then the elementary operator is m isometry on the hilbert schmidt operator ideal in this paper we show that the converse of this result is also true we also give a necessary and sufficient condition for the generalized derivation to be an m isometry the sufficiency follows from results on the sum of m isometries and nilpotent operators in two recent papers

existence of solution of an infinite system of generalized fractional differential equations by darbo s fixed point theorem abstract in our manuscript the existence of solution of an infinite system of three point boundary value problem of generalized fractional derivative in the caputo sense has been discussed in the linear space c 0 1 c 0 we obtain existence result by employing darbo fixed point theorem using the hausdorff measure of noncompactness

numerical computation of the nonlinear feedback operators for the nonquadratic time variant optimal control problems in this paper a reliable numerical algorithm for the nonlinear feedback operators for the time variant optimal control with nonquadratic criteria is constructed our approach rests mainly on the modified adomian decomposition method the convergence of the decomposition method as applied to the synthesis equations is investigated the proposed scheme avoids the complexity provided by using other techniques

existence of non subnormal polynomially hyponormal operators in 1950 p r halmos motivated in part by the successful development of the theory of normal operators introduced the notions of subnormality and hyponormality for bounded hilbert space operators an operator t is subnormal if it is the restriction of a normal operator to an invariant subspace t is hyponormal if t t tt it is a simple matrix calculation to verify that subnormality implies hyponormality but the converse is false one reason is that subnormality is invariant under polynomial calculus indeed analytic functional calculus while hyponormality is not if one then defines t to be polynomially hyponormal when p t is hyponormal for every polynomial p e c z the following question arises naturally

adomian decomposition method for solution of nonlinear differential algebraic equations in m m hosseini adomian decomposition method with chebyshev polynomials appl math comput in press an efficient modification of the adomian decomposition method was presented by using chebyshev polynomials also in m m hosseini adomian decomposition method for solution of differential algebraic equations j comput appl math in press solution of linear differential algebraic equations was considered by adomian decomposition method in this paper standard and modified adomian decomposition methods are applied to non linear differential algebraic equations the schemes are tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

non perturbative analytical solution of the general lotka volterra three species system the lotka volterra equations are solved for the general three species system using the adomian decomposition comparisons are shown for a prey predator model whose exact solution is available as well as for perturbative solution by murty and rao

the adomian decomposition method in turning point problems in this paper the decomposition method is applied to boundary value problems of ordinary differential equations with a parameter exhibiting turning points

on a measure of noncompactness in the holder space ck γ ω and its application abstract in this article based on the concept of relative compactness in the holder space c k where k 0 0 1 and is a compact subset of r n we present a new measure of noncompactness on c k moreover as an application we study the existence of solution of a nonlinear integral equation in the holder space by applying darbo fixed point theorem

adomian decomposition method for solving bvps for fourth order integro differential equations the adomian decomposition method adm is applied to solve both linear and nonlinear boundary value problems bvps for fourth order integro differential equations the numerical results obtained with minimum amount of computation or mathematics compare reasonably well with exact solutions

numerical study of lorenz s equation by the adomian method abstract in this paper we use the decomposition method of adomian for solving differential systems coming from physics meteorology we also give a comparison between the runge kutta method and the decomposition technique furthermore we reconfirm the famous butterfly effect

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

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

solving a system of nonlinear fractional differential equations using adomian decomposition adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations dxiyi x ni x y1 yn yi k 0 cki 0 k i 1 i n and dxi denotes caputo fractional derivative some examples are solved as illustrations using symbolic computation

the tanh coth and the sine cosine methods for kinks solitons and periodic solutions for the pochhammer chree equations abstract in this paper the tanh coth method and the sine cosine method are used for a reliable treatment of the pochhammer chree equations which include a variety of models travelling wave solutions of distinct structures namely bell shaped solitons kink shaped solitons and periodic solutions are formally derived the two methods demonstrate power reliability and efficiency

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

adomian decomposition approach to a sir epidemic model with constant vaccination strategy over the years diligent vaccination campaigns have resulted in high levels of permanent immunity against the childhood disease among the population in this article a sir model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is developed the qualitative analysis reveals the vaccination reproductive number for disease control and eradication adomian decomposition method is also employed to compute an approximation to the solution of the non linear system of differential equations governing the problem maple is used to carry out the computations graphical results are presented and discussed quantitatively to illustrate the solution