Accession Number : ADA114597

Title :   Difference Methods for Parabolic History Value Problems.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Markowich,Peter

PDF Url : ADA114597

Report Date : Mar 1982

Pagination or Media Count : 29

Abstract : This paper is concerned with one-step difference methods for parabolic history value problems in one space variable. These problems, which have the feature that the evolution of the solution is influenced by 'all its past' occur in the theory of viscoelastic liquids (materials with 'memory'). The history dependence is represented by a Volterra-integral in the equation of motion. Using recently obtained existence results and smoothness assumptions on the solution, we derive a local stability and convergence result for a Crank-Nicolson-type difference scheme by interpreting the linearized scheme as perturbation of a strictly parabolic scheme without memory term. Second order convergence is shown on sufficiently small time intervals. The presented approach carries over to other one-step difference methods like implicit Euler schemes.

Descriptors :   *Boundary value problems, *Equations of motion, *Parabolas, History, Linear differential equations, Euler angles, Stability, Time intervals, Viscoelasticity, Theory, Convergence, Liquids

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE