Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 09, pp 1-12.
Title: Numerical solution of a parabolic equation with a
weakly singular positive-type memory term
Author: Marian Slodicka (Univ. of the Federal Armed Forces Munich, Germany)
Abstract:
We find a numerical solution of an initial and boundary value problem.
This problem is a parabolic integro-differential equation whose integral
is the convolution product of a positive-definite weakly singular
kernel with the time derivative of the solution.
The equation is discretized in space by linear finite elements, and in time
by the backward-Euler method. We prove existence and uniqueness of the
solution to the continuous problem, and demonstrate that some regularity
is present. In addition, convergence of the discrete sequence of
iterations is shown.
Submitted March 14, 1997. Published June 4, 1997.
Math Subject Classification: 65R20, 65M20, 65M60.
Key Words: integro-differential parabolic equation;
full discretization.