Numerical approximation based on Bernouli polynomials for solving second-order hyperbolic telegraph equations

Matinfar, Mashallah; Abdollahi Lashaki, Hamideh; Akbari, Mozhgan; Ahmed, Hany

doi:10.22080/cjms.2023.25277.1653

Numerical approximation based on Bernouli polynomials for solving second-order hyperbolic telegraph equations

Document Type : Review Article

Authors

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

² science facaulty, Farhangian University, Tehran, Iran

³ Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

⁴ Department of Mathematics, Faculty of Technology and Education, Helwan University, Cairo-Egypt

10.22080/cjms.2023.25277.1653

Abstract

In this paper, a practical matrix method is presented for solving a particular type of telegraph equations. This procedure is based on Bernouli Polynomials. This matrix method with collocation suited nodes, decreases the supposed equations into system of algebric equations with unknown Bernouli coefficients. The obtained system is solved and approximate solutions are achieved. The well-conditioning of problems is also considered. The indicated method creates the well-onditioned problems. Some numerical problems are comprised to confirm the efficacy and fitting of the suggested method. The presented technique is easy to implement and produces accurate results. The precision of the method is demonstrated by measuring the errors between exact solutions and approximate solutions for each problem.

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