numerical solution of one-dimensional differential equations by weighted residual method using bernoulli wavelets

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.