Error and extrapolation of a compact LOD method for parabolic differential equations

Authors:
Yuan-Ming Wang
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 3
Cited 1

Numerical Analysis of Coupled Systems of Nonlinear Parabolic Equations

SIAM Journal on Numerical Analysis
High-Order Compact ADI Methods for Parabolic Equations

Computers & Mathematics with Applications
Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems

Journal of Computational Physics

Quantified Score

Hi-index	7.30

Visualization

Abstract

This paper is concerned with a compact locally one-dimensional (LOD) finite difference method for solving two-dimensional nonhomogeneous parabolic differential equations. An explicit error estimate for the finite difference solution is given in the discrete infinity norm. It is shown that the method has the accuracy of the second-order in time and the fourth-order in space with respect to the discrete infinity norm. A Richardson extrapolation algorithm is developed to make the final computed solution fourth-order accurate in both time and space when the time step equals the spatial mesh size. Numerical results demonstrate the accuracy and the high efficiency of the extrapolation algorithm.