Numerical Solution for Semi Linear Hyperbolic Differential Equations

Valmir BAME; Lulezim HANELLI

doi:10.21276/ijirem.2019.6.4.1

Abstract

A Numerical method is proposed for the solution of semi linear hyperbolic differential equation. The method is of the characteristic type and it is particularly helpful in case of discontinuous initial data. The new proposal is elaborated and implemented in Matlab for canonical case of differential equation. Then, its local and global order of convergence is conventionally estimated using canonical examples. The method is extended for the solution of a wave equation with a non-classical right boundary condition, where special treatment of the right boundary is required.

Keywords

Characteristic Method, Conventional Order, Boundary Conditions, Semi Linear Hyperbolic, Linear Hyperbolic.

Reference

[1] Darmawijoyo, W., Van Horssen, W. and Clement, Ph. (2003). "On a Rayleigh wave equation with boundary damping," in Nonlinear Dynamics, 33, pp. 399-429.

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[3] Trangestein, J. A. (2007). Numerical solution of hyperbolic partial differential equations, Cambridge University Press, New York

Cites this article as

V. BAME, L. H. , "Numerical Solution for Semi Linear Hyperbolic Differential Equations", International Journal of Innovative Research in Engineering & Management (IJIREM), Vol-6, Issue-4, Page No-28-32, 2019. Available from: https://doi.org/10.21276/ijirem.2019.6.4.1