Numerical solution of systems of first order stiff oscillatory differential equations using diagonally implicit super class of block backward differentiation formula

This paper introduces the development and application of a diagonally implicit ۳-point method based on a superclass of the Block Backward Differentiation Formula (۳DSBBDF) for solving systems of first-order stiff Oscillatory Differential Equations (ODEs) in Initial Value Problems (IVPs). By varying the free parameter  within the stability interval , different families of ۳-point block methods can be generated. Notably, when  in the proposed scheme, the ۳DSBBDF method reduces to the existing fifth-order ۳-point Block Backward Differentiation Formula (۳DBBDF), making ۳DBBDF a special case of the new approach. The method is specifically designed to effectively capture oscillatory behavior while maintaining high-order accuracy and stability. Both theoretical analysis and numerical experiments confirm the superior performance of ۳DSBBDF in solving stiff oscillatory problems compared to the existing ۳DBBDF solver in the literature.

کلیدواژه ها:

Stiff Oscillatory Differential Equations ، Diagonally Implicit Method ، Block Backward Differentiation Formula ، High-Order Accuracy and Stability