Sixth-Order Hybrid Block Method for the Numerical Solution of First Order Initial Value Problems

Hybrid block method of order six is proposed in this paper for the numerical solution of first order initial value problems. The method is based on collocation of the differential system and interpolation of the approximate at the grid and off-grid points. The procedure yields five consistent finite difference schemes which are combined as simultaneous numerical integrators to form block method. The method is found to be zero-stable hence convergent. The accuracy of the method is shown with some standard first order initial value problems. 2010 Mathematics Subject Classifications:65L05,65L06,65L07 and 65L20 Keywords: Multistep, collocation, Finite Differential Method,simultaneous numerical integrators, block, accuracy, consistent and convergent