Numerical solution of one-dimensional differential equations by weighted residual method using Bernoulli wavelets

Abstract

This paper presents the method of solving one-dimensional differential equations through the weighted residual technique, employing Bernoulli wavelets as the basis functions. These wavelets serve as the foundation for the calculation of numerical solutions for one-dimensional differential equations. The numerical outcomes are contrasted with those from current techniques and the precise solution. A selection of numerical test problems is included to demonstrate the practicality and efficiency of the proposed approach.

Keywords

• weighted residual method
• bernoulli wavelets
• one-dimensional differential equations
• boundary conditions
• finite difference method