A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials

Abstract

In this article, a collocation approximation is investigated for approximate solutions of hyperbolic telegraph partial differential equations (HTPDEs). The method is based on evenly spaced collocation points and Pell–Lucas polynomials (PLPs). The form of solution, derivatives of unknown function in equation and conditions are expressed in matrix forms which depend on PLMs. By the help of these matrix forms and collocation points, problem is reduced to a system of linear algebraic equations. In addition, error analysis is performed for method. Thus, errors are bound by an upper bound. By making the applications of these techniques, the computed outcomes are offered in tables and graphs. Also the obtained outcomes by method are also compared with outcomes of other methods in the literature. These comparisons show that our method is more influential than other methods. All results have been computed by the aid of a code generated in MATLAB.

Keywords

• Collocation method
• error analysis
• hyperbolic equations
• partial differential equations
• Pell–Lucas polynomials
• 35L20