In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...

He’s variational iteration method is applied to fourth-order parabolic partial differential equations with variable coefficients. To illustrate the ability and reliability of the method, some examples are given, revealing its effectiveness and simplicity. c © 2007 Published by Elsevier Ltd

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

In this paper we deal with a nonlinear singular integral inequality which arises in the study of partial differential equations. The integral term is non local in time and space and the kernel involved is also singular in both the time and the space variable. The estimates we prove may be used to establish (global) existence and asymptotic behavior results for solutions of the corresponding pro...

A fundamental solution (or Green’s function) is a singular solution of a governing partial differential equation (PDE). They can be constructed easily when the PDE has constant coefficients. They are useful for reducing boundary-value problems to boundary integral equations (BIEs). We begin by describing simple properties of fundamental solutions, and then comment on the use and construction of...

Stochastic solutions is a robust technique previously used to obtain new exact for deterministic nonlinear partial differential equations as well numerical algorithms suited parallel computing. Here it proposed solution method driven by distribution-valued noises. Two examples are worked out in detail.