Numerical Applications of the Block Method to Higher Order Oscillatory Real-Life Problems

Abstract

This study explores the development and application of block hybrid method for solving second-order Ordinary Differential Equations (ODEs). The focus is on enhancing the accuracy and efficiency of solving Initial Value Problems (IVPs), particularly for second order oscillatory differential equations. A new computational block hybrid method is proposed and analyzed, with comparisons made against existing methods to highlight improvements in stability and convergence. The application of the new method is demonstrated through several test cases, showing their effectiveness in handling challenging differential equations, such as those arising in physics and engineering. Results indicate significant advantages in both computational speed and error reduction when using the proposed method over traditional numerical techniques.