On formule plusieurs methodes de Galerkin a temps discret pour des equations integrodifferentielles paraboliques

Finite element methods for parabolic and hyperbolic partial integro-differential equations

Parameter determination in a partial differential equation from the overspecified data

The spectral methods for parabolic Volterra integro-differential equations

In this paper, an effective numerical method for solving nonlinear Volterra partial integro-differential equations is proposed. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function which is the “memory” of problem. This method is based on radial basis functions (RBFs) and finite difference method (FDM) which provide the approximate solution. These techniques play the important role to reduce a nonlinear partial integro-differential equation to a linear system of equations. Some illustrative examples are shown to describe the method. Numerical examples confirm the validity and efficiency of the presented method.

A numerical solution of nonlinear parabolic-type Volterra partial integro-differential equations using radial basis functions

Numerical blow-up analysis of linearly implicit Euler method for nonlinear parabolic integro-differential equations

The progress of compression of a water saturated porous medium is derivable from the equation of continuity,Darcy's law, and an appropriate effective stressdilation relationship. Theories of secondary consolidation assume that the effective stress-dilatation relationship is time-dependent. One form of this type of characterization is a system of linear viscoelastic models. The system chosen consists of an elastic element in series with an arbitrary number ofKelvin units. The formulation of this system is a differential-integral equation. The integral portions of the equation are a series of convolution integrals. A finite difference scheme is developed in which the single governing differential-integral equation is broken up into a system of equations of the heat conduction andEuler types. A stability theorem is proved.

G. J. Habetler

Papers

A finite difference method for analyzing the compression of poro-viscoelastic media