Symbolic solutions for boundary value problems using Maple

A simple technique based on finite differences is presented for obtaining symbolic solutions for boundary value problems (BVPs). The governing equations for the node points are expressed in matrix form and the dependent variables (e.g. concentration) at both the boundaries (both at x = 0 and x = 1) are taken as unknown constants. The solution is obtained by finding the matrix inverse using Maple. The unique aspect of the technique presented here is that the solution obtained is valid for various boundary conditions (both linear and nonlinear) and geometries. Both linear ordinary differential equations (ODEs) and partial differential equations (PDEs) with linear and non-linear boundary conditions are treated in this paper. Solutions analytical in time are obtained for PDEs. (C) 2000 Elsevier Science Ltd. All rights reserved.