A 14-Order Hybrid Block Method in Variable Step-Size Mode for Solving Second-Order Initial Value Problems

The search for efficient higher order methods is a constant goal in numerical analysis. In this paper, a higher order two-step hybrid block method is presented to directly solve second-order initial value problems in ordinary differential equations. In addition to the higher order, the proposed method has been formulated in variable step-size mode to extract its best performance. Comparisons with other methods in the literature show the good accuracy it can provide. Theoretical aspects such as linear stability and convergence analysis are also discussed.