A Reliable Numerical Treatment of Differential Equations via Hybrid Bernstein and Improved Block-Pulse Functions

Abstract

Recently, the authors attempted to solve integral equations using hybrid improved block pulse and Bernstein functions. However, this is the first article to present a technical coupling between improved block-pulse functions and Bernstein functions for solving differential equations. The current method converts differential equations into an algebraic system that can be solved using traditional methods. To demonstrate the validity of this new approach, some numerical tests are provided. The findings demonstrated that the method is both promising and highly accurate.