DERIVATION AND ANALYSIS OF BLOCK HYBRID METHOD FOR SOLVING INITIAL VALUE PROBLEMS IN OSCILLATORY DIFFERENTIAL EQUATIONS

Abstract

The Block Hybrid Method is a numerical technique for solving ordinary differential equations (ODEs), particularly effective for stiff and oscillatory systems. This paper introduces a new method designed to handle challenges posed by equations like the Malthusian Growth Model and Prothero-Robinson equation, which are difficult to solve using conventional methods due to stiffness and rapid oscillations. Derived using power series approximation, the method is analyzed for order, error constant, consistency, and zero stability, proving to be convergent, consistent, and zero-stable. Numerical examples demonstrate its superior accuracy and stability compared to existing methods, making it a valuable tool for solving complex initial value problems in real-world applications.