A PARALLEL MESH CHOPPING ALGORITHM FOR A CLASS OF 2-POINT BOUNDARY-VALUE-PROBLEMS

A parallel algorithm for the class of two-point boundary value problem s y '' = f(x, y), y(0) = A, y(1) = B with partial derivative f/partial derivative y greater than or equal to 0 and partial derivative f/part ial derivative y continuous on [0, 1] x (infinity, infinity) is presen ted. Using an idea similar to that in [1], we divide [0, 1] into p dif ferent divisions, each division consisting of N or (N + 1) (N small) u nequal intervals. A high-order finite difference scheme developed for general nonuniform mesh is now applied to the above class of TPBVP's o n each of the p divisions and leads to an N x N or (N - 1) x (N - 1) s ystem of linear or nonlinear equations which is solved on p processors (p a power of 2) simultaneously.