A comparative study of the Daubechies wavelet based new Galerkin and Haar wavelet collocation methods for the numerical solution of differential equations

Abstract

In this paper, we have made an attempt to comparative study of the existing Haar wavelet collocation method with proposed new wavelet-Galerkin method for the solution of differential equations. The solutions obtained using proposed scheme are comparably good and give higher accuracy than existing ones with exact solution by increasing the level of resolution.To yield the solutions of differential equations using usal wavelet-Galerkin require use of connection coefficients, which takes large computational complexities and time consumption. The proposed scheme is rather simple and avoids the above complexities, which is demonstrated through the some of the test problems.