a comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations in this paper we conduct a comparative study between the modified decomposition method and two of the traditional methods for analytic treatment of nonlinear integral and integro differential equations the proper implementation of the modified method can dramatically minimize the size of work if compared to existing traditional techniques the analysis is accompanied by examples that demonstrate the comparison and show the pertinent features of the modified technique

the finite element approximation of hamilton jacobi bellman equations abstract this paper deals with the finite element approximation of hamilton jacobi bellman equations we establish a convergence and a quasi optimal l error estimate involving a weakly coupled systems of quasi variational inequalities for the solution of which an interative scheme of monotone kind is introduced and analyzed

the finite element approximation of hamilton jacobi bellman equations the noncoercive case this paper deals with the piecewise linear approximation of hamilton jacobi bellman equations with noncoercive operators we establish an l error estimate developing a very simple approach based mainly on a discrete l stability property with respect to the data for the corresponding discrete coercive problem

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

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

solution of bvps for fourth order integro differential equations by using homotopy perturbation method in this study the homotopy perturbation method proposed by ji huan he is applied to solve both linear and nonlinear boundary value problems for fourth order integro differential equations the analysis is accompanied by numerical examples the results show that the homotopy perturbation method is of high accuracy more convenient and efficient for solving integro differential equations

a new computational method for volterra fredholm integral equations abstract the main purpose of this article is to demonstrate the use of the adomian decomposition method for mixed nonlinear volterra fredholm integral equations a bound is also given for the adomian decomposition series finally numerical examples are presented to illustrate the implementation and accuracy of the decomposition method

a new proof for the existence and uniqueness of the discrete evolutionary hjb equations in this paper we establish a new proof for the existence and uniqueness of the discrete solution of evolutionary hjb equations which can be approximated by a weakly coupled system of coercive elliptic quasi variational inequalities ovis for that some properties of the presented algorithm cf e g boulaaras and haiour 2013 boulbrachene and haiour 2001 using the theta scheme with respect to the t variable combined with a finite element spatial approximation are proved

picard s iterative method for nonlinear advection reaction diffusion equations picard s iterative method for the solution of nonlinear advection reaction diffusion equations is formulated and its convergence proved the method is based on the introduction of a complete metric space and makes uses of a contractive mapping and banach s fixed point theory from picard s iterative method the variational iteration method is derived without making any use at all of lagrange multipliers and constrained variations some examples that illustrate the advantages and shortcomings of the iterative procedure presented here are shown

the variational iteration method for solving linear and nonlinear systems of pdes in this work the variational iteration method vim is used for analytic treatment of the linear and nonlinear systems of partial differential equations the method reduces the calculation size and overcomes the difficulty of handling nonlinear terms numerical examples are examined to highlight the significant features of the vim method the method shows improvements over existing numerical techniques

asymptotic error expansion for the nystro m method for a nonlinear volterra fredholm integral equation in this paper we study the numerical solution of general nonlinear mixed volterra fredholm integral equations by the trapezoidal nystrom method it focuses on the derivation and analysis of asymptotic error expansion of the nystrom solution providing the basis for richardson s extrapolation this will greatly increase the accuracy of the numerical solution some numerical results are given to illustrate this theory

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

derivation of the adomian decomposition method using the homotopy analysis method abstract adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems it has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits however very little has been done to address the mathematical foundation of the method and its error analysis in this article the mathematical derivation of the method using the homotopy analysis method is presented in addition an error analysis is addressed as well as the convergence criteria

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

the combined reproducing kernel method and taylor series for handling nonlinear volterra integro differential equations with derivative type kernel abstract the reproducing kernel method is applied to volterra nonlinear integro differential equations in this technique the nonlinear term is replaced by its taylor series the exact solution is represented in the form of series in the reproducing hilbert kernel space the approximation solution is expressed by n term summation of reproducing kernel functions some numerical examples are solved in two different spaces and parameters of n measurements of the experimental data is an indications of stability and convergence on the reproducing kernel

he s homotopy perturbation method an effective tool for solving nonlinear integral and integro differential equations in this paper we conduct a comparative study among he s homotopy perturbation method and three traditional methods for an analytic and approximate treatment of nonlinear integral and integro differential equations the proper implementation of he s homotopy perturbation method can extremely minimize the size of work if compared to existing traditional techniques the analysis is accompanied by examples that demonstrate the comparison and shows the pertinent features of the homotopy perturbation technique

on the numerical solution of nonlinear volterra fredholm integral equations by collocation methods particular cases of nonlinear mixed volterra fredholm integral equations of the second kind arise in the mathematical modeling of the spatio temporal development of an epidemic this paper is concerned with the numerical solution of general integral equations of this type by continuous time and discrete time spline collocation methods its focus is on the derivation and analysis of methods of high order of convergence

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

iterative and non iterative methods for non linear volterra integro differential equations iterative and non iterative methods for the solution of nonlinear volterra integro differential equations are presented and their local convergence is proved the iterative methods provide a sequence solution and make use of fixed point theory whereas the non iterative ones result in series solutions and also make use of fixed point principles by means of integration by parts and use of certain integral identities it is shown that the initial conditions that appear in the iterative methods presented here can be eliminated and the resulting iterative technique is identical to the variational iteration method which is derived here without making any use at all of lagrange multipliers and constrained variations it is also shown that the formulation presented here can be applied to initial value problems in ordinary differential volterra s integral and integro differential pantograph and nonlinear and linear algebraic equations a technique for improving accelerating the convergence of the iterative methods presented here is also presented and results in a lipschitz constant that may be varied as the iteration progresses it is shown that this acceleration technique is related to preconditioning methods for the solution of linear algebraic equations it is also argued that the non iterative methods presented in this paper may not competitive with iterative ones because of possible cancellation errors if implemented numerically an analytical continuation procedure based on dividing the interval of integration into disjoint subintervals is also presented and its limitations are discussed

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

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

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

fourth order integro differential equations using variational iteration method in this paper the variational iteration method proposed by ji huan he is applied to solve both linear and nonlinear boundary value problems for fourth order integro differential equations the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the variational iteration method is of high accuracy more convenient and efficient for solving integro differential equations