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

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.

Automated summary

This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation, considering both explicit and implicit schemes working at two time levels and having three point spatial support. By discussing classical schemes as examples, the paper shows the possible implications of the modified equation on the properties of the numerical methods being considered.