a new analytical and numerical treatment for singular two point boundary value problems via the adomian decomposition method based on the adomian decomposition method a new analytical and numerical treatment is introduced in this research to investigate linear and non linear singular two point bvps the effectiveness of the proposed approach is verified by several linear and non linear examples

continuous functions on the plane regular after one blowing up we study rational functions admitting a continuous extension to the real affine space first of all we focus on the regularity of such functions exhibiting some nice properties of their partial derivatives afterwards since these functions correspond to rational functions which become regular after some blowings up we work on the plane where it suffices to blow up points and then we can count the number of stages of blowings up necessary in the latest parts of the paper we investigate the ring of rational continuous functions on the plane regular after one stage of blowings up in particular we prove a positivstellensatz without denominator in this ring

application of he s variational iteration method and adomian s decomposition method to the fractional kdv burgers kuramoto equation in this work the fractional kdv burgers kuramoto equation is studied he s variational iteration method vim and adomian s decomposition method adm are applied to obtain its solution comparison with ham is made to highlight the significant features of the employed methods and their capability of handling completely integrable equations

distance spectra of graphs a survey abstract in 1971 graham and pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems they also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph computing the distance characteristic polynomial and its coefficients was the first research subject of interest thereafter the eigenvalues attracted much more attention in the present paper we report on the results related to the distance matrix of a graph and its spectral properties

piecewise homotopy methods for nonlinear ordinary differential equations abstract piecewise homotopy perturbation methods are developed for the solution of nonlinear ordinary differential equations these methods are based on the introduction of an artificial or book keeping parameter and the expansion of the solution in a power series of this parameter and provide analytical solutions in open intervals which are smooth everywhere three piecewise adaptive homotopy perturbation methods based on the use of either a fixed number of approximants and a variable step size a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size are presented and applied to eight nonlinear ordinary differential equations it is shown that piecewise adaptive homotopy perturbation methods predict essentially the same solutions as matlab s variable step variable order solvers and variable order transition matrix techniques provided that five term approximations of the decomposition method are applied to both the displacement and the velocity it is also shown that piecewise homotopy perturbation techniques that use three term approximations to both the displacement and the velocity provide essentially the same results as those obtained with a second order accurate time linearization technique when the same step is employed in both schemes

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

a new approach to the wave equation an application of the decomposition method abstract in the present paper the inhomogeneous wave equation is solved quickly easily and elegantly by adomian s decomposition method

the distance signatures of the incidence graphs of affine resolvable designs abstract in this note we determined the distance signatures of the incidence matrices of affine resolvable designs this proves a conjecture by kohei yamada

approximation by piecewise regular maps abstract a real algebraic variety w of dimension m is said to be uniformly rational if each of its points has a zariski open neighborhood which is biregularly isomorphic to a zariski open subset of r m let l be any nonnegative integer we prove that every map of class c l from a compact subset of a real algebraic variety into a uniformly rational real algebraic variety can be approximated in the c l topology by piecewise regular maps of class c k where k is an arbitrary integer satisfying k l next we derive consequences regarding algebraization of topological vector bundles

on the solution of partial differential equations with specified boundary conditions abstract the decomposition method is applied to solution of partial differential equations in two and three dimensions with specified boundary conditions

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

a new symbolic computational approach to singular initial value problems in the second order ordinary differential equations this paper presents a new symbolic algorithm to compute the singular initial value problem of second order ordinary differential equations using adomian decomposition method the algorithm has been implemented in the computer algebra system maple to facilitate the application of this method a number of examples are presented to demonstrate the computation efficiency of the program

approximation of maps into spheres by piecewise regular maps of class c k the aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise regular maps of class mathcal c k where k is an arbitrary nonnegative integer

revisit on partial solutions in the adomian decomposition method solving heat and wave equations the adomian decomposition method is considered in application to heat and wave equations the so called partial solution technique is used it is shown that the fundamental equation of the method is well defined only for certain types of boundary conditions in cases involving inhomogeneous boundary conditions improper results may be obtained by former method this paper presents a further insight into partial solutions in the decomposition method and the resolution of such cases

arc wise analytic stratification whitney fibering conjecture and zariski equisingularity abstract in this paper we show whitney s fibering conjecture in the real and complex local analytic and global algebraic cases for a given germ of complex or real analytic set we show the existence of a stratification satisfying a strong real arc analytic with respect to all variables and analytic with respect to the parameter space trivialization property along each stratum we call such a trivialization arc wise analytic and we show that it can be constructed under the classical zariski algebro geometric equisingularity assumptions using a slightly stronger version of the zariski equisingularity we show the existence of whitney s stratified fibration satisfying the conditions b of whitney and w of verdier our construction is based on the puiseux with parameter theorem and a generalization of whitney s interpolation for algebraic sets our construction gives a global stratification we also present several applications of the arc wise analytic trivialization mainly to the stratification theory and the equisingularity of analytic set and function germs in the real algebraic case for an algebraic family of projective varieties we show that the zariski equisingularity implies local constancy of the associated weight filtration

a new approach to the heat equation an application of the decomposition method abstract the author s decomposition method adomian stochastic systems academic press new york 1983 nonlinear stochastic operator equations academic press new york in press bellman and adomian partial differential equations methods for their treatment and solution reidel dordrecht 1984 adomian j comput appl math 2 1984 225 230 shown elsewhere to provide computable accurate approximate convergent solutions to nonlinear stochastic operator equations is applied to the heat equation

an adaptation of adomian decomposition for numeric analytic integration of strongly nonlinear and chaotic oscillators a novel form of an explicit numeric analytic technique is developed for solving strongly nonlinear oscillators of engineering interest the analytic part of this technique makes use of adomian decomposition method adm but unlike other analytical solutions it does not rely on the functional form of the solution over the whole domain of the independent variable instead it discretizes the domain and solves multiple ivps recursively adm uses a rearranged taylor series expansion about a function and finds a series of functions which add up to generate the required solution the present method discretizes the axis of the independent variable and only collects lower powers of the chosen step size in series solution each function constituting the series solution is found analytically it is next shown that the modified adm can be used to obtain the analytical solution in a piecewise form for nonlinear oscillators such a piecewise solution is valid only within a chosen time step an attempt has been made to address few issues like the order of local error and convergence of the method emphasis has been on the application of the present method to a number of well known oscillators the method has the advantage of giving a functional form of the solution within each time interval thus one has access to finer details of the solution over the interval this is not possible in purely numerical techniques like the runge kutta method which provides solution only at the two ends of a given time interval provided that the interval is chosen small enough for convergence it is shown that the present technique successfully overcomes many limitations of the conventional form of adm the present method has the versatility and advantages of numerical methods for being applied directly to highly nonlinear problems and also have the elegance and other benefits of analytical techniques

solving frontier problems modelled by nonlinear partial differential equations abstract we present a further development of the decomposition method 1 2 which leads to a single efficient and global method of solving linear or nonlinear ordinary or partial differential equations for initial value or boundary value problems no linearization perturbation or resort to discretized methods is involved potential savings in computation are very large perhaps six orders of magnitude in some cases and important implications exists for modeling and computational analysis it is to be noted that once we realize that we can be less constrained by the mathematics by removing the necessity of techniques such as linearization perturbation or discretization to make analysis and computation of the models feasible and practical we become able to develop more sophisticated and realistic models modeling effectively means retention of essential features while striving for simplicity so that the resulting equations can be solved with fewer limitations imposed to achieve tractibility the models can be more realistic and we have a convinient and global technique for solution

exact and numerical soliton solutions of some nonlinear physical models we consider two types of variant water wave equations and the solitary wave solutions of them are constructed by using the adomian decomposition we also made a numerical comparison of the equations

a new method for solving singular initial value problems in the second order ordinary differential equations singular initial value problems linear and nonlinear homogeneous and nonhomogeneous are investigated by using adomian decomposition method the solutions are constructed in the form of a convergent series a new general formula is established the approach is illustrated with few examples

efficient algorithms to solve singular integral equations of abel type in the present paper we obtain the approximate solution of abel s integral equation by using the following powerful efficient but simple methods i he s homotopy perturbation method hpm ii modified homotopy perturbation method mhpm iii adomian decomposition method adm and iv modified adomian decomposition method madm the validity and applicability of these techniques are illustrated through various particular cases which demonstrate their efficiency and simplicity in solving these types of integral equations compared with the other existing methods

experimentation with two step adomian decomposition method to solve evolution models the two step adomian decomposition method tsadm is derived by separate the standard adomian decomposition method into two steps although the tsadm needs only a slight variation from the standard adomian decomposition method experimentation shows that the tsadm is also promising for systems of inhomogeneous differential and integral equations hyperbolic partial differential equations and singular initial value problems

curve rational functions let w be a subset of the set of real points of a real algebraic variety x we investigate which functions f w rightarrow mathbb r are the restrictions of rational functions on x we introduce two new notions curve rational functions i e continuous rational on algebraic curves and arc rational functions i e continuous rational on arcs of algebraic curves we prove that under mild assumptions the following classes of functions coincide continuous hereditarily rational introduced recently by the first named author curve rational and arc rational in particular if w is semialgebraic and f is arc rational then f is continuous and semialgebraic we also show that an arc rational function defined on an open set is arc analytic i e analytic on analytic arcs furthermore we study rational functions on products of varieties as an application we obtain a characterization of regular functions finally we get analogous results in the framework of complex algebraic varieties

extensions of arc analytic functions we prove that every arc analytic semialgebraic function on an arc symmetric set x in mathbb r n admits an arc analytic semialgebraic extension to the whole mathbb r n

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

spline methods for the solution of fourth order parabolic partial differential equations in this paper a fourth order non homogeneous parabolic partial differential equation that governs the behaviour of a vibrating beam is solved by using a new three level method based on parametric quintic spline in space and finite difference discretization in time stability analysis of the method has been carried out it has been shown that by suitably choosing the parameters most of the previous known methods for homogeneous and non homogeneous cases can be derived from our method we also obtain two new high accuracy schemes of o k 4 h 6 and o k 4 h 8 and two new schemes which are analogues of jain s formula for the non homogeneous case comparison of our results with those of some known methods show the superiority of the present approach

continuous rational maps into spheres let x be a compact nonsingular real algebraic variety we prove that if a continuous map from x into the unit p sphere is homotopic to a continuous rational map then under certain assumptions it can be approximated in the compact open topology by continuous rational maps as a byproduct we also obtain some results on approximation of smooth submanifolds by nonsingular subvarieties

on the convergence of adomian decomposition method here a simple method to determine the rate of convergence of adomian decomposition method is introduced the proposed method is used to compare between the rate of convergence of standard and modified proposed by wazwaz a m wazwaz a new method for solving singular initial value problems in the second order ordinary differential equations appl math comput 128 2002 45 57 adomian methods for solving lane emden singular problem furthermore with providing some examples the aforementioned cases are dealt with numerically

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

the noisy convergence phenomena in decomposition method solutions abstract a damped oscillating convergence to a correct solution sometimes observed in decomposition method solutions of differential and partial differential equation is investigated

a computational algebraic investigation of the decomposition method for time dependent problems the convergence of the decomposition method as applied to time dependent problems governed by the heat or wave equations is investigated numerically using computational algebraic techniques

a proof of kurdyka s conjecture on arc analytic functions we prove a conjecture of kurdyka stating that every arc symmetric semialgebraic set is precisely the zero locus of an arc analytic semialgebraic function this implies in particular that arc symmetric semialgebraic sets are in one to one correspondence with radical ideals of the ring of arc analytic semialgebraic functions

the inertia and energy of distance matrices of complete k partite graphs abstract for a distance matrix d g its inertia is the triple of integers n d n 0 d n d where n d n 0 d n d denote the number of positive 0 negative eigenvalues of d g respectively the d energy is the sum of the absolute eigenvalues of d g in this paper we first study the inertia of distance matrices of complete k partite graphs then as applications we not only prove a conjecture proposed by caporossi et al 2009 in 5 in a different way from stevanovic et al 2013 11 but also obtain the formula of the d energy of the remaining complete k partite graphs at last we obtain the graphs with the maximum resp minimum d energy among all the complete k partite graphs with n vertices

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

exact solutions for heat like and wave like equations with variable coefficients in this paper adomian decomposition method is presented for solving heat like and wave like models with variable coefficients the method is demonstrated for a variety of problems in one and higher dimensional spaces where exact solutions are obtained the results obtained in all cases show the reliability and the efficiency of this method

a reliable technique for solving the weakly singular second kind volterra type integral equations abstract in this paper the adomian decomposition method and the phenomenon of the self canceling noise terms are used for solving the weakly singular volterra type linear and nonlinear integral equations the solution obtained is in the form of a convergent power series with elegantly computable terms comparing this scheme with many collocation type methods that use the nonpolynomial basis shows that the present approach is effective and powerful many test modeling problems from mathematical physics linear and nonlinear are discussed to illustrate the effectiveness and the performance of the decomposition method

numerical solution of two dimensional nonlinear differential equation by homotopy perturbation method abstract in this paper an application of homotopy perturbation method is applied to solve the nonlinear two dimensional wave equation the analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components the non homogenous equation is effectively solved by employing the phenomena of the self canceling noise terms where sum of components vanishes in the limit comparing the methodology with some known techniques shows that the present approach is powerful and reliable its remarkable accuracy properties are finally demonstrated by an example

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

semi algebraic geometry with rational continuous functions let x be a real algebraic subset of mathrm mathbb r n we investigate the theory of algebraically constructible functions on x and the description of the semi algebraic subsets of x when we replace the polynomial functions on x by some rational continuous functions on x

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

an artificial parameter decomposition method for nonlinear oscillators applications to oscillators with odd nonlinearities abstract a method for obtaining series solutions of nonlinear second order ordinary differential equations based on the introduction of an artificial parameter is presented and shown to be identical to the well known adomian s decomposition technique the method is formulated in both integral and differential forms for the determination of the limit cycle of oscillators with odd nonlinearities two differential forms and one integral form of the artificial parameter method are presented these versions are based on introducing a linear stiffness term with an unknown frequency and the use of either the original independent variable or a new independent variable that depends linearly on the unknown frequency of the oscillator the three formulations provide identical results and their application to eight oscillators with odd nonlinearities shows that the artificial parameter technique presented in this paper predicts the same frequency of oscillation as the harmonic balance and iterative techniques as well as modified linstedt poincare methods however the method presented here is based on the introduction of an artificial parameter and does not require the presence of small perturbation parameters in the ordinary differential equation it is also shown that two and three level iterative methods yield the same frequency of oscillation as the artificial parameter technique presented in this paper provided that the initial iterate of the former coincides with the leading order solution of the latter and only one iteration of iterative techniques and only the second approximation of the artificial parameter method are determined

new recurrence algorithms for the nonclassic adomian polynomials in this article we present new algorithms for the nonclassic adomian polynomials which are valuable for solving a wide range of nonlinear functional equations by the adomian decomposition method and introduce their symbolic implementation in mathematica beginning with rach s new definition of the adomian polynomials we derive the explicit expression for each class of the adomian polynomials e g a email protected k 1 mf k u 0 z m k for the class ii iii and iv adomian polynomials where the z m k are called the reduced polynomials these expressions provide a basis for developing improved algorithmic approaches by introducing the index vectors the recurrence algorithms for the reduced polynomials are suitably deduced which naturally lead to new recurrence algorithms for the class ii and class iii adomian polynomials mathematica programs generating these classes of adomian polynomials are subsequently presented computation shows that for computer generation of the class iii adomian polynomials the new algorithm reduces the running times compared with the definitional formula we also consider the number of summands of these classes of adomian polynomials and obtain the corresponding formulas finally we demonstrate the versatility of the four classes of adomian polynomials with several examples which include the nonlinearity of the form f t u explicitly depending on the argument t

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

piecewise regular maps let v w be real algebraic varieties that is up to isomorphism real algebraic sets and x subseteq v some subset a map from x into w is said to be regular if it can be extended to a regular map defined on some zariski locally closed subvariety of v that contains x furthermore a continuous map f x rightarrow w is said to be piecewise regular if there exists a stratification mathscr s of v such that for every stratum s in mathscr s the restriction of f to each connected component of x cap s is a regular map by a stratification of v we mean a finite collection of pairwise disjoint zariski locally closed subvarieties whose union is equal to v assuming that the subset x of v is compact we prove that every continuous map from x into a grassmann variety or a unit sphere can be approximated by piecewise regular maps as an application we obtain a variant of the algebraization theorem for topological vector bundles if the variety v is compact and nonsingular we prove that each continuous map from v into a unit sphere is homotopic to a piecewise regular map of class mathscr c k where k is an arbitrary nonnegative integer

the decomposition method for forward and backward time dependent problems the convergence of the decomposition method as applied to time dependent problems governed by the heat wave and beam equations is investigated for both forward direct and backward inverse problems it is shown that for forward problems the convergence is faster than for backward problems

explicit solutions for differential equations advantages exist in use of the decomposition method 1 2 for solutions of differential equations even for the trivial case of solution of first order separable differential equations the decomposition solutions are more useful because of the resulting convenient computable explicit solutions the same techniques and benefits apply to the algebraic equations obtained by transform methods in solving differential equations a comparison is made also between solutions by integrating factor and decomposition and it is shown that decomposition is an obvious recourse when an integrating factor is not available to show advantages of the procedure a differential equation solvable by several methods and involving a logarithmic nonlinearity is solved by adomian s decomposition for comparisons the decomposition method will also solve higher order differential equations and partial differential equations with logarithmic or even composite nonlinearities 2 when the other methods fail

a reliable treatment for mixed volterra fredholm integral equations the main goal of this paper is to demonstrate the use of the modified decomposition method for mixed nonlinear volterra fredholm integral equations the modified method combined with the noise terms phenomena may provide the exact solution by using two iterations only two numerical illustrations are given to show the pertinent features of the technique

convergence of adomian s decomposition method periodic temperatures abstract the convergence of adomian s decomposition method 1 as applied to periodic temperature fields in heat conductors is investigated

application of the adomian decomposition method for two dimensional parabolic equation subject to nonstandard boundary specifications in this work we are concerned with the solution of a nonlocal boundary value problem an approach is presented for solving the two dimensional parabolic partial differential equation subject to integral boundary specifications the main objective is to propose an alternative method of solution one not based on finite difference methods or finite element schemes or spectral techniques the aim of the present paper is to investigate the application of the adomian decomposition method for solving the two dimensional linear parabolic partial differential equation with nonlocal boundary specifications replacing the classical boundary conditions the adomian decomposition method is used by many researchers to investigate several scientific applications and requires less work if compare with the traditional techniques the introduction of this idea as will be discussed not only provides the solution in a series form but it also guarantees considerable saving of the calculations volume the solutions will be handle more easily quickly and elegantly without linearizing the problem by implementing the decomposition method rather than the standard methods for the exact solutions in this approach the solution is found in the form of a convergent power series with easily computed components the adomian decomposition scheme is easy to program in applied problems and provides immediate and convergent solutions without any need for linearization or discretization to give a clear overview of the methodology we have selected illustrative example

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

on grothendieck rings and algebraically constructible functions we investigate grothendieck rings appearing in real geometry notably for arc symmetric sets and focus on the relative case in analogy with the properties of the ring of algebraically constructible functions defined by mccrory and parusinski we study in particular the duality and link operators including their behaviour with respect to motivic milnor fibres with signs

a new modification of adomian decomposition method for solving a kind of evolution equation in this paper we propose a new modification of adomian decomposition method for solving a kind of evolution equation the modification will improve the convergence of the series solution the validity of the modified technique is verified through illustrative examples

arc spaces motivic measure and lipschitz geometry of real algebraic sets we investigate connections between lipschitz geometry of real algebraic varieties and properties of their arc spaces for this purpose we develop motivic integration in the real algebraic set up we construct a motivic measure on the space of real analytic arcs we use this measure to define a real motivic integral which admits a change of variables formula not only for the birational but also for generically one to one nash maps as a consequence we obtain an inverse mapping theorem which holds for continuous rational maps and more generally for generically arc analytic maps these maps appeared recently in the classification of singularities of real analytic function germs finally as an application we characterize in terms of the motivic measure germs of arc analytic homeomorphism between real algebraic varieties which are bi lipschitz for the inner metric

a homotopy perturbation technique for solving partial differential equations of fractional order in finite domains abstract in this paper a homotopy perturbation technique is proposed to solve a class of initial boundary value problems of partial differential equations of arbitrary fractional orders over finite domains the basic idea of this technique is to utilize both the initial and boundary conditions in the recursive relation of the solution scheme so that we can obtain a good approximate solution numerical examples are presented to illustrate the validity of the proposed technique

the decomposition method for cauchy advection diffusion problems in this paper the solution of cauchy problems for the advection diffusion equation is obtained using the decomposition method in the case when the flow velocity is constant an analytical solution can be derived whilst for variable flow velocity symbolic numerical computations need to be performed

solving nonlocal initial boundary value problems for the lotka von foerster model in this paper we present a new approach to solve nonlocal initial boundary value problems for the lotka von foerster model subject to initial and nonlocal boundary conditions of integral type we first transform the given nonlocal initial boundary value problem into an equivalent local initial boundary value problem then we apply a modified adomian decomposition method which permits convenient resolution of these problems also a new method is developed to solve this nonlocal model which reduces it to an equivalent local initial boundary value problem for a system of ordinary differential equations

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 convergence analysis of the adm and an application in this paper by considering the decomposition scheme we solve the modified korteweg de vries equation mkdv for short for the initial condition we prove the convergence of adomian decomposition method adm applied to the mkdv equation

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

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

solutions to the non homogeneous parabolic problems by the extended hadm in this paper we extend the homogeneous adomain decomposition method hadm introduced by jang bongsoo jang exact solutions to one dimensional non homogeneous parabolic problems by the homogeneous decomposition method appl math comput 186 2 2007 969 979 to solve non homogeneous parabolic partial differential equations with variable coefficients the new modified technique provides the less computational work as well as easy calculation in obtaining the accurate approximations compared with the standard adm illustrative examples show the excellent performance for the new modified decomposition method

modified adomian decomposition method for specific second order ordinary differential equations in this paper an efficient modification of adomian decomposition method is introduced for solving second order ordinary differential equations the proposed method can be applied to singular and nonsingular problems the scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed method

a new approach to the nonlinear advection problem an application of the decomposition method abstract in this paper the nonlinear advection problem is solved easily and elegantly by using the adomian s decomposition method the exact solution is quickly obtained by observing the appearance of the self canceling noise terms whose sum vanishes in the limit comparison with other existing techniques shows that the present approach is highly accurate

solving nonlocal initial boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the adomian decomposition method in this paper we present a new approach to solve nonlocal initial boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations subject to initial and nonlocal boundary conditions of integral type we first transform the given nonlocal initial boundary value problems of integral type for the linear and nonlinear parabolic and hyperbolic partial differential equations into local dirichlet initial boundary value problems and then use a relatively new modified adomian decomposition method adm furthermore we investigate the fourier adomian method which also does not require any a priori assumptions on the solution for the solution of nonlocal initial boundary value problems combined with our new approach several examples are presented to demonstrate the efficiency of the adm