TITLE:
A Computational Study with Finite Difference Methods for Second Order Quasilinear Hyperbolic Partial Differential Equations in Two Independent Variables
AUTHORS:
Pavlos Stampolidis, Maria Ch. Gousidou-Koutita
KEYWORDS:
Finite Difference Method, CTCS Method, Crank-Nicolson Method, ω-Method, Numerical Method of Characteristics, Wave Equation
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.11,
November
13,
2018
ABSTRACT: In this paper we consider the numerical method of characteristics for the numerical solution of initial value problems (IVPs) for quasilinear hyperbolic Partial Differential Equations, as well as the difference scheme Central Time Central Space (CTCS), Crank-Nicolson scheme, ω scheme and the method of characteristics for the numerical solution of initial and boundary value prob-lems for the one-dimension homogeneous wave equation. The initial deriva-tive condition is approximated by different second order difference quotients in order to examine which gives more accurate numerical results. The local truncation error, consistency and stability of the difference schemes CTCS, Crank-Nicolson and ω are also considered.