Legendre multiscaling functions for solving the one‐dimensional parabolic inverse problem

作者：S. A. Yousefi, Mehdi Dehghan · 发表于：Numerical Methods for Partial Differential Equations · 年份：2009 · DOI：10.1002/num.20430 · 被引用次数：23 · 研究领域：Advanced Mathematical Modeling in Engineering、Numerical methods in inverse problems、Differential Equations and Boundary Problems

Abstract An inverse problem concerning diffusion equation with a source control parameter is investigated. The approximation of the problem is based on the Legendre multiscaling basis. The properties of Legendre multiscaling functions are first presented. These properties together with Galerkin method are then utilized to reduce the inverse problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009