New algorithm for nonclassical parabolic problems based on the reproducing kernel method

Abstract

Purpose: In this paper, a new algorithm is presented for solving one-dimensional parabolic partial differential equations subject to integral conditions. Methods: The algorithm is based on the transverse method of lines and the reproducing kernel method. The transverse method of lines can reduce a one-dimensional parabolic partial differential equation subject to integral conditions to a series of ordinary differential equations(ODEs) with integral boundary conditions. The reproducing kernel method is a relative new analytical technique, which can solve successfully ODEs with integral boundary conditions.