Galerkin Method for the Numerical Solution of One-Dimensional Differential Equations using Gegenbauer Wavelets

Differential equations are important because for many physical systems, one can, subject to suitable idealizations, formulate a differential equation that describes how the system changes in time. Understanding the solutions of the differential equation is then of paramount interest. Wavelet analysis is a new branch of mathematics widely applied in signal analysis, image processing, numerical analysis, etc. This paper presents the Galerkin method for the numerical solution of one-dimensional differential equations using weight functions are Gegenbauer wavelets (GWGM). The performance of the proposed method is better than that of the existing ones in terms of convergence. Some of the test problems are taken to demonstrate the validity and efficiency of the proposed method.