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2022 | OriginalPaper | Chapter

Simple Finite Difference Procedures

Authors : Jürgen Steppeler, Jinxi Li

Published in: Mathematics of the Weather

Publisher: Springer International Publishing

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Abstract

This chapter gives a few definitions of standard numerical schemes to be used for comparison or as part of the schemes to be described in later chapters. As this book is mainly about spatial discretization, the fourth-order Runge–Kutta scheme is used in tests for time discretization. A rather comprehensive set of possibilities is given in Durran (Numerical methods for fluid dynamics: with applications to geophysics, 2nd edn. Springer, New York, pp. 35–146, 2010), along with an analysis of many standard numerical temporal schemes. This information is given here to make this book self-contained. It is readable with basic knowledge of mathematics and without previous knowledge of numerics and this chapter is overlapping with Durran (Numerical methods for fluid dynamics: with applications to geophysics, 2nd edn. Springer, New York, pp. 35–146, 2010) for the convenience of the reader.

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previous chapter Introduction
next chapter Local- Galerkin Schemes in 1D
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Metadata
Title
Simple Finite Difference Procedures
Authors
Jürgen Steppeler
Jinxi Li
Copyright Year
2022
Book
Mathematics of the Weather

Print ISBN: 978-3-031-07237-6

Electronic ISBN: 978-3-031-07238-3

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-031-07238-3_2