Legendre multiscaling functions for solving the one‐dimensional parabolic inverse problem
S. A. Yousefi, Mehdi Dehghan · Numerical Methods for Partial Differential Equations · 2009
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