TITLE:
Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients
AUTHORS:
Yanmeng Sun, Qing Yang
KEYWORDS:
Two-Dimensional First-Order Hyperbolic Equation, Variable Coefficients, Upwind Difference Schemes, Fourier Method, Stability and Error Estimation
JOURNAL NAME:
Engineering,
Vol.13 No.6,
June
30,
2021
ABSTRACT: In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.