Modified equation for a class of explicit and implicit schemes solving one-dimensional advection problem

0540783 - MÚ 2022 RIV CZ eng J - Journal Article
Bodnár, Tomáš - Fraunié, P. - Kozel, K.
Modified equation for a class of explicit and implicit schemes solving one-dimensional advection problem.
Acta Polytechnica. Roč. 61, SI (2021), s. 49-58. ISSN 1210-2709. E-ISSN 1805-2363
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : advection equation * finite difference * modified equation
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.14311/AP.2021.61.0049

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.
Permanent Link: http://hdl.handle.net/11104/0318381