MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM

Tomáš Bodnár; Philippe  Fraunié; Karel  Kozel

doi:10.14311/AP.2021.61.0049

Authors

Tomáš Bodnár Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Material Engineering, Karlovo náměstí 293/13, Prague, 12000, Czech Republic; Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 115 67 Prague, Czech Republic
Philippe Fraunié Université de Toulon, Mediterranean Institute of Oceanography - MIO, BP 20132 F-83957 La Garde cedex, France
Karel Kozel Czech Technical University in Prague, Faculty of Mechanical Engineering, Karlovo Náměstí 13, 121 35 Prague, Czech Republic

DOI:

https://doi.org/10.14311/AP.2021.61.0049

Keywords:

Modified equation, finite difference, advection equation

Abstract

This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods.

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