IJPAM: Volume 52, No. 5 (2009)

A NUMERICAL SOLUTION FOR THE FIRST-ORDER
HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS
BY USING A FACTORIZED DIAGONAL
NON-POLYNOMIAL APPROXIMATION

Kemal Altiparmak
Department of Mathematics
Faculty of Education
University of Ege
Bornova, Izmir, 35100, TURKEY
e-mail: kemal.altiparmak@ege.edu.tr


Abstract.In this paper, a numerical method for solving first-order hyperbolic partial differential equations has been developed. These methods are developed approximating to the first-order spatial derivative through second-order backward difference approximations and first-order hyperbolic partial differential equation is reduced to the system of the ordinary differential equations using the method of lines. A matrix exponential function in the recurrence relation of the exact solution is approximated with a factorized non-polynomial approximation having real roots. A recursive algorithm is developed and tested on a personal computer with Maple V Release 5 for a numerical example.

Received: April 18, 2009

AMS Subject Classification: 6506, 41A20

Key Words and Phrases: finite difference, Pade approximation, matrix exponential function, non-polynomial approximation with real roots, factorization, first-order hyperbolic partial differential equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 5