Computation of two time-dependent coefficients in a parabolic partial differential equation subject to additional specifications

• Published in: International journal of computer mathematics Vol. 87; no. 5; pp. 997 - 1008
• Main Authors: Saadatmandi, Abbas, Dehghan, Mehdi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.04.2010; Taylor & Francis Ltd
• Subjects: Algebra; Approximation; Derivatives; inverse problem; Mathematical analysis; Mathematical models; Matrices; operational matrix; parabolic partial differential equations; Partial differential equations; Polynomials; simultaneous parameter determination; Specifications; tau method
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160802253958

In this paper, we consider the problem of the simultaneous determination of time-dependent coefficients in a one-dimensional partial differential equation. The main aim is to apply the tau technique to determine unknown coefficients in a time-dependent partial differential equation. Our approach consists of reducing the problem to a set of algebraic equations by expanding the approximate solution in terms of shifted Legendre polynomials with unknown coefficients. The operational matrices of integral and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.