HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS  

作　　者：R.K.MOHANTY VENU GOPAL 

机构地区：[1]Department of Mathematics University of Delhi,Delhi-110007,India

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2012年第2期1-18,共18页建模、仿真和科学计算国际期刊（英文）

基　　金：“The University of Delhi”under research grant No.Dean(R)/R&D/2010/1311.

摘　　要：In this paper,we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyper-bolic partial differential equation of the form utt=A(x,y,t)uxx+B(x,y,t)uyy+g(x,y,t,u,ux,uy,ut),0<x,y<1,t>0 subject to appropriate initial and Dirichlet boundary conditions.We use only five evaluations of the function g and do not require any fictitious points to discretize the differential equation.The proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally stable.Numerical results are provided to illustrate the usefulness of the proposed method.

关 键 词：Nonlinear hyperbolic equation variable coefficients arithmetic average type approximation wave equation in polar coordinates van der Pol equation telegraphic equation maximum absolute errors. 

分 类 号：O17[理学—数学]