Ritz-Galerkin method for solving a parabolic equation with non-local and time-dependent boundary conditions

摘要

The paper is devoted to the investigation of a parabolic partial differential equation with non-local and time-dependent boundary conditions arising from ductal carcinoma in situ model. Approximation solution of the present problem is implemented by the Ritz-Galerkin method, which is a first attempt at tackling parabolic equation with such non-classical boundary conditions. In the process of dealing with the difficulty caused by integral term in non-local boundary condition, we use a trick of introducing the transition function G(x,t) to convert non-local boundary to another non-classical boundary, which can be handled with the Ritz-Galerkin method. Illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright (c) 2015 John Wiley & Sons, Ltd.