Symbolic solutions for boundary value problems using Maple

A simple technique based on finite differences is presented for obtaining s ymbolic solutions for boundary value problems (BVPs). The governing equatio ns for the node points are expressed in matrix form and the dependent varia bles (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 mat rix inverse using Maple. The unique aspect of the technique presented here is that the solution obtained is valid for various boundary conditions (bot h linear and nonlinear) and geometries. Both linear ordinary differential e quations (ODEs) and partial differential equations (PDEs) with linear and n on-linear boundary conditions are treated in this paper. Solutions analytic al in time are obtained for PDEs. (C) 2000 Elsevier Science Ltd. All rights reserved.