Numerical Application of Enright's Linear Multistep Method on Oscillatory Differential Equations - Agbo, Christiana Ene; Ayinde, Abdullahi Muhammed; Chuseh, John Ahmadu; Ugwu, Ugochukwu Clemen (Faculty of Natural and Applied Sciences Journal of Mathematical Modeling and Numerical Simulation, 2025)
Oscillatory differential equations play a vital role in modeling natural and physical phenomena in fields such as biology, circuit theory, and fluid dynamics. These equations often lack analytical solutions, necessitating numerical methods for resolution. This study focuses on the development and application of a continuous Enright linear multistep block hybrid method to solve first-order oscillatory differential equations. The method leverages interpolation and collocation techniques to generate a high-order, stable, and accurate numerical scheme. The basic properties, including order, consistency, zero-stability, convergence and the region of absolute stability, are analyzed to validate the method. Numerical experiments are conducted to compare the new method's accuracy and computational efficiency against existing approaches, demonstrating its superior performance in solving oscillatory problems.