Development of Hybrid Block Methods for Oscillatory Solutions of Second-Order Differential Equations

This study explores the application of hybrid block method in solving oscillatory second-order initial value problems (IVPs), a category of differential equations relevant in modeling various real-life phenomena, such as mechanical and electrical oscillations. Traditional numerical methods often face challenges in accuracy and stability when applied to oscillatory problems, prompting a need for advanced methods like hybrid block method. This research developed a hybrid block method that offers improved error control, stability and convergence for oscillatory differential equations. Error analysis is conducted to assess the method's effectiveness, comparing it with existing approaches to highlight its robustness in handling oscillatory behavior. The proposed method demonstrates an expanded stability region, making it suitable for complex, real-world applications that require high precision. The study's findings emphasize the potential of block hybrid methods in advancing numerical solutions for differential equations, providing valuable insights for further research and application in science and engineering