Numerical solution of boundary value problems using Hermite wavelet-Galerkin method.

1st International E-Conference on Recent Developments in Science, Engineering and Information Technology on 23rd to 25th September, 2020 Department of Computer Science, DDE, Madurai Kamaraj University, Tamil Nadu, India. International Journal of Computer Science (IJCS) Published by SK Research Group of Companies (SKRGC)

Abstract

In this paper, we proposed Numerical solution of boundary value problems using Hermite Wavelet-Galerkin Method. Here, we used weight functions as a Hermite wavelets that are assumed basis elements which allow us to obtain the numerical solutions of boundary value problems. The numerical solutions obtained by this method are compared with the exact solution and existing methods. Some of the problems are given to demonstrate the effectiveness and accuracy of the proposed method.

References

[1] Arrora S., Brar Y.S., Kumar S., Haar wavelet matrices for the numerical solutions of differential equations, International Journal of Computer Applications, 97(18) (2014), 33-36.

[2] Mosevic J. W., Identifying Differential Equations by Galerkin's Method, Mathematics of Computation, 31(1977), 139-147.

[3] Daubeshies I., Ten lectures on Wavelets, Philadelphia: SIAM, 1992.

[4] Ali A., Iqbal M.A., Mohyud-Din S.T., Hermite Wavelets Method for Boundary Value Problems, International Journal of Modern Applied Physics, 3(1) (2013), 38-47 .

[5] Shiralashetti, S.C., Kumbinarasaiah, S., Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems, Alexandria Engineering Journal (2017) xxx, xxx–xxx(Article in press).

[6] Saha R. S., Gupta A.K., A numerical investigation of time fractional modified Fornberg-Whitham equation for analyzing the behavior of water waves. Appl Math Comput 266 (2015), 135–148.

[7] Cicelia J.E., Solution of Weighted Residual Problems by using Galerkin’s Method, Indian Journal of Science and Technology,7(3) (2014), 52–54.

[8] Shiralashetti S. C., Kantli M.H., Deshi A. B., A comparative study of the Daubechies wavelet based new Galerkin and Haar wavelet collocation methods for the numerical solution of differential equations, Journal of Information and Computing Science, 12(1) (2017), 052-063.

[9] Erturk V.S., Differential transformation method for solving differential equations of lane-emden type, Mathematical and Computational Applications, 12(3) (2007), 135-139.

 

Keywords

Hermite wavelets; Galerkin method; Numerical solution; Finite difference method