Author(s)

Yanmeng Sun, Qing Yang

School of Mathematics and Statistics, Shandong Normal University, Jinan, China.

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.

Two-Dimensional First-Order Hyperbolic Equation, Variable Coefficients, Upwind Difference Schemes, Fourier Method, Stability and Error Estimation

Sun, Y. and Yang, Q. (2021) Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients. Engineering, 13, 306-329. doi: 10.4236/eng.2021.136023.