ONE-STEP SECOND DERIVATIVES METHOD WITH INTRA-STEP POINTS FOR SOLVING INITIAL VALUE PROBLEM IN ORDINARY DIFFERENTIAL EQUATION

Abstract

An optimized one-step hybrid block method for the numerical solution of first-order initial value problems is constructed. The method takes into consideration two and four intra-step 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 and seven algebraic order. Some standard examples such as Riccati equation, system of linear equation and chemical equation are discussed to show the accuracy of the proposed method over the existing method in the literature