Composite spectral method for solution of the diffusion equation with specification of energy

Many physical subjects are modeled by nonclassical parabolic boundary value problems with nonlocal boundary conditions replacing the classic boundary conditions. In this article, we introduce a new numerical method for solving the one-dimensional parabolic equation with nonlocal boundary conditions. The approximate proposed method is based upon the composite spectral functions. The properties of composite spectral functions consisting of terms of orthogonal functions are presented and are utilized to reduce the problem to some algebraic equations. The method is easy to implement and yields very accurate result. (C) 2007 Wiley Periodicals, Inc.