Leveraging feed-forward neural networks to enhance the hybrid block derivative methods for system of second-order ordinary differential equations

Abstract

This study introduces an innovative method combining discrete hybrid block techniques and artificial intelligence to enhance the solution of second-order Ordinary Differential Equations (ODEs). By integrating feed-forward neural networks (FFNN) into the hybrid block derivative method (HBDM), the modified approach shows improved accuracy and efficiency compared to traditional methods. Through comprehensive comparisons with exact and existing solutions, the study demonstrates the effectiveness of the proposed approach. The evaluation, utilizing root mean square error (RMSE), confirms its superior performance, robustness, and applicability in diverse scenarios. This research sets a new standard for solving complex ODE systems, offering promising avenues for future research and practical implementations.