Optimization of one step block method with three hybrid points for solving first-order ordinary differential equations

Abstract

An optimized one-step hybrid block method for the numerical solution of first-order initial value problems is presented. The method takes into consideration three hybrid points which are chosen appropriately to optimize the local truncation errors of the main formulas for the block. The method is zero-stable and consistent with fifth algebraic order. Some numerical examples are discussed to show the efficiency and the accuracy of the proposed method.