Composite Bernoulli-Laguerre collocation method for a class of hyperbolic telegraph-type equations

Abstract

In this work, we introduce an efficient Bernoulli-Laguerre collocation method for solving a class of hyperbolic telegraph-type equations in one dimension. Bernoulli and Laguerre polynomials and their properties are utilized to reduce the aforementioned problems to systems of algebraic equations. The proposed collocation method, both in spatial and temporal discretizations, is successfully developed to handle the two-dimensional case. In order to highlight the effectiveness of our approachs, several numerical examples are given. The approximation techniques and results developed in this paper are appropriate for many other problems on multiple-dimensional domains, which are not of standard types.