Fibonacci Wavelets based Galerkin Method for Numerical Solu tion of Boundary Value Problems

Abstract

The present work discusses using Fibonacci Wavelets (FWGM) in the Galerkin technique for solving Boundary Value Problems (BVPs). In this innovative approach, Fibonacci wavelets are employed as weight functions, serving as essential elements that simplify the computation of numerical solutions for BVPs. These wavelets offer unique properties that enhance the accuracy and efficiency of the Galerkin method, making it a powerful tool for tackling complex BVPs.

To evaluate the performance of the proposed method, the numerical solutions obtained through FWGM were compared with those derived from other well-established techniques, as well as the exact solutions. This comparative analysis is crucial for demonstrating the reliability and precision of the Fibonacci Wavelet-based Galerkin method. By selecting a range of BVPs, the study provides a comprehensive overview of the method's effectiveness and practicality in various scenarios.

The results of the comparisons indicate that the FWGM not only matches but often surpasses the accuracy of traditional methods. This highlights the potential of Fibonacci wavelets in offering a robust and efficient alternative for solving BVPs. The comprehensive examination of multiple boundary value problems demonstrates the adaptability and practicality of the suggested method, verifying its importance as a noteworthy breakthrough in the numerical solution of boundary value problems. The manuscript underscores the practicality and effectiveness of the FWGM, positioning it as a promising method for future research and application in the field.