Solving the inverse problem of identifying an unknown source term in a parabolic equation

Authors:
A. Shidfar;A. Babaei;A. Molabahrami
Affiliations:
School of Mathematics, Iran University of Science and Technology, PO Box 16846 13114, Tehran, Iran;School of Mathematics, Iran University of Science and Technology, PO Box 16846 13114, Tehran, Iran;School of Mathematics, Iran University of Science and Technology, PO Box 16846 13114, Tehran, Iran and Department of Mathematics, Ilam University, PO Box 69315516, Ilam, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

The inverse problem of determining an unknown source term in a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition is considered. The series pattern solution of the problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and identifying the unknown source term is derived. Finally, several examples are presented to illustrate this method.