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.
Description:
To tackle real-world challenges across engineering, biological sciences, physical sciences, electronics, and other disciplines, researchers frequently encounter initial value problems, as noted by. Many practical problems in engineering and science are initially formulated as differential equations before resolution. These equations typically involve derivatives, establishing a connection between an independent variable, a dependent variable and one or more differential coefficients concerning.
