A parallel mesh chopping algorithm for a class of two-point boundary value problems

A parallel algorithm for the class of two-point boundary value problems y″ = f(x,y), y(0) = A, y(1) = B with and continous on [0,1] × (−∞, ∞) is presented. Using an idea similar to that in [1], we divide [0,1] into p different divisions, each division consisting of N or (N + 1) (N small) unequal intervals. A high-order finite difference scheme developed for general nonuniform mesh is now applied to the above class of TPBVPʹs on each of the p divisions and leads to an N × N or (N − 1) × (N − 1) system of linear or nonlinear equations which is solved on p processors (p a power of 2) simultaneously.