Haar Wavelet Collocation Method for Telegraph Equations with Different Boundary Conditions

Abstract

In this article, we study the Haar wavelet operational matrix approach for finding the numerical solutions of hyperbolic telegraph equations under suitable initial and boundary conditions. It has been approximated in both space and time using the Haar wavelets series with unknown coefficients. The advantage of the method is that it reduces the original problems to a set of algebraic equations that can be solved using standard methods. The precision and efficacy of the numerical method are shown via numerical examples. It has been shown experimentally that the approach is straightforward, precise, when compared to some of the current numerical methods.

Key words and phrases. Collocation point, Dirichlet boundary condition, Haar wavelet, Neuman boundary conditions, Operational matrices, Telegraph equations.

2020 Mathematics Subject Classification. 42C40; 65M99; 65T60; 35L10