Derivation of a new block fifth order method for numerical solution of first order initial value problems

Abstract

A new block method of order five for the numerical solution of initial value problems is derived. The coefficients of the matrix of the method are chosen such that low power of the blocksize appears in the principal local truncation error. The stability polynomial is shown to be a perturbation of order explicit Runge-Kutta method. Key words: Predictor-corrector methods, ordinary differential equations, block methods.