Weighted residual method for the numerical solution of boundary value problems utilizing Fibonacci wavelets

The boundary value problems (BVPs) are crucial because they model real world phenomena governed by differential equations with constraints at the edges (boundaries) of a domain unlike initial value problems (IVPs) which focus on a single point. The basic idea behind wavelets is to analyze according to scale. "Wavelets" are functions used to represent data or other functions that meet specific mathematical conditions. This work proposes a numerical solution for BVPs using the weighted residual technique with Fibonacci wavelets (WRMFW). In this case Fibonacci wavelets are used as weight functions that assume basis elements which allow us to obtain the numerical solution of BVPs. Obtained numerical solutions using this method are compared with existing methods and exact solutions. There are a few BVPs to demonstrate the validity and applicability of the proposed method.