An Implicit Second-Order Block Method for Simulation Betiss and Stiefel Oscillatory Differential Equation

This research shows the development and simulation of an implicit second-order block method for solving Betiss and Stiefel differential equations. The method's fundamental properties including order, consistency, and stability were rigorously analyzed, confirming its theoretical robustness under standard numerical analysis principles. Through comparative testing on oscillatory differential equations, the proposed method demonstrated enhanced accuracy and computational efficiency over existing approaches. The results reveal its superior performance in terms of error reduction and stability, making it a viable improvement for long-term simulations of stiff and oscillatory systems.