Numerical solutions of telegraph equations with the Dirichlet boundary condition

Ashyralyev A., Turkcan K. T., Köksal M. E.

3rd International Conference on Analysis and Applied Mathematics (ICAAM), Almaty, Kazakhstan, 7 - 10 September 2016, vol.1759 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1759
  • Doi Number: 10.1063/1.4959669
  • City: Almaty
  • Country: Kazakhstan
  • Keywords: Telegraph equations, Numerical solutions, Error analysis, DIFFERENCE SCHEME
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.