Papanikos, G. and Gousidou-Koutita, M. (2015) A Computational Study with Finite Element Method and Finite Difference Method for 2D Elliptic Partial Differential Equations. Applied Mathematics, 6, 2104-2124.
https://doi.org/10.4236/am.2015.612185

has been cited by the following article:

• 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.