A New Modified Fifth-Order Implicit Block Method for Solving Stiff and Oscillatory Problems

Abstract

A new fifth-order modified implicit 3-point super class of block backward differentiation formula for solving oscillatory problems and systems of stiff ordinary differential equations (ODEs) is developed. The method is order five. The stability and convergence properties of the method demonstrate that the method is consistent, zero-stable and almost A-stable which are necessary and sufficient conditions to integrate the stiff systems and oscillatory ODEs. Numerical experiments reveal that the proposed method delivers superior performance compared to existing conventional 3-point Block Backward Differentiation Formula (3BBDF) and 3-point Super Class of Block Backward Differentiation Formula (3SBBDF) methods, making it a robust and efficient tool for addressing stiff problems.