A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations. Issue 6 (4th August 2020)

• Record Type: Journal Article
• Authors: Asif, Muhammad; Haider, Nadeem; Al‐Mdallal, Qasem; Khan, Imran
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 6(2020)
• Page Start: 1962
• Page End: 1981
• Publication Date: 2020-08-04
• Subjects: collocation method -- Haar wavelet -- one‐ and two‐dimensional hyperbolic TEs -- partial differential equations; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22512
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: We have developed a new numerical method based on Haar wavelet (HW) in this article for the numerical solution (NS) of one‐ and two‐dimensional hyperbolic Telegraph equations (HTEs). The proposed technique is utilized for one‐ and two‐dimensional linear and nonlinear problems, which shows its advantage over other existing numerical methods. In this technique, we approximated both space and temporal derivatives by the truncated Haar series. The algorithm of the method is simple and we can implement easily in any other programming language. The technique is tested on some linear and nonlinear examples from literature. The maximum absolute errors (MAEs), root mean square errors (RMSEs), and computational convergence rate are calculated for different number of collocation points (CPs) and also some 3D graphs are also drawn. The results show that the proposed technique is simply applicable and accurate.