Analysis of a fourth-order compact ADI method for a linear hyperbolic equation with three spatial variables

Authors:
Dingwen Deng;Chengjian Zhang
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, People's Republic of China 430074 and College of Mathematics and Information Science, Nanchang Hangkong ...;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, People's Republic of China 430074
Venue:
Numerical Algorithms
Year:
2013

Citing 6
Cited 0

A compact finite-difference scheme for solving a one-dimensional heat transport equation at the microscale: 431

Journal of Computational and Applied Mathematics
A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation

Journal of Computational and Applied Mathematics
A new unconditionally stable ADI compact scheme for the two-space-dimensional linear hyperbolic equation

International Journal of Computer Mathematics
Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

International Journal of Computer Mathematics
Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations

Applied Numerical Mathematics
Maximum norm error estimates of efficient difference schemes for second-order wave equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is concerned with a three-level alternating direction implicit (ADI) method for the numerical solution of a 3D hyperbolic equation. Stability criterion of this ADI method is given by using von Neumann method. Meanwhile, it is shown by a discrete energy method that it can achieve fourth-order accuracy in both time and space with respect to H 1- and L 2-norms only if stable condition is satisfied. It only needs solution of a tri-diagonal system at each time step, which can be solved by multiple applications of one-dimensional tri-diagonal algorithm. Numerical experiments confirming the high accuracy and efficiency of the new algorithm are provided.