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https://doi.org/10.1007/s10915-020-01171-7

has been cited by the following article:

• 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.