Fourth-Order Block Methods for the Numerical Solution of First Order Initial Value Problems

Block methods of order two and three for the numerical solution of initial value problems are extended to four order. The proposed two fourth order block methods might be efficient for implementation in multiprocessor computers. The matrix coefficients like block methods of order two and three of these methods are chosen so that lower powers of blocksize appear in the principle local truncation errors. The stability polynomial is shown to be a perturbation of the (p + 1)ᵗʰ order explicit Runge-Kutta method, scaled according to block size. In order to show the linear stability properties of the block predictor corrector methods, the maximum absolute errors using Type I and Type II methods with blocksize $k = 10$ and various step sizes are investigated numerically. 2000 Mathematics Subject Classification. 65L05, 65Y05