Numerical procedure for the determination of an unknown parameter in a parabolic equation

Abstract

A numerical procedure for an inverse problem of determining unknown source parameter of one-dimensional parabolic equation subject to the specification of the solution at internal point along with the usual initial boundary conditions is considered. By using some transformation the problem is reformulated to a nonlocal parabolic problem. Some numerical examples using the proposed numerical procedure are presented.

Keywords:

• Parabolic equation
• Inverse problem
• Unknown coefficient
• Finite-difference method

AMS Subject Classifications:

• 35K15
• 35Q99
• 39A10

C.R. Categories:

• G1.8