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A general class of finite-difference methods for the linear transport equation. (English) Zbl 1092.65070

Summary: A wide family of finite-difference methods for the linear advection equation, based on a six-point stencil, is presented. The family depends on three parameters and includes most of the classical linear schemes. A stability and consistency analysis is carried out. Numerical examples show the performance of the different methods according to the choice of the parameters. The problem of the determination of the parameters providing the “best approximation” is also addressed.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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