An inverse problem for the damped generalized regularized long wave equation

Abstract

In this article, we consider an inverse problem related to the damped generalized regularized long wave equation with noisy data. We study numerically this problem by applying the quartic B-spline and Haar wavelet methods combined with the Tikhonov regularization method. We investigate the stability and the convergence analysis of this problem and show that $O(k^2+h^3)$ and $O(\frac{1}{M})$ are the convergence rates of the quartic B-spline method and the Haar wavelet method, respectively. The numerical results, by a comparative study, show that an excellent estimation of the unknown functions of the mentioned inverse problem.

Keywords:

• Regularized long-wave equation
• inverse problem
• quartic B-spline
• Haar wavelet method

2010 Mathematics Subject Classifications:

• 35Q53
• 65D07
• 68W25
• 35R30
• 65T60

Acknowledgments

Authors are very grateful to referees for reading the paper carefully and for comments and suggestions which improved the quality of paper.

Disclosure statement

No potential conflict of interest was reported by the authors.