Parallel Mesh Division Algorithm For General Linear Two Point Boundary Value Problems

In this paper, a parallel computational method proposed for the numerical solutions of two point semilinear boundary value problems is extended for general linear boundary value problems with natural boundary conditions. A division method is used which divides [0,1] into p different subdivisions, each division consisting of N or (N +1) (N small) unequal intervals. A high order finite difference method for general nonuniform mesh is then applied to the TPBVP on each of p divisions and leads to an N × N or (N -1)× (N-1) system of linear equations which is solved on p processors simultaneously. Numerical examples are provided to show the accuracy and speedup thus achieved.