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Erschienen in:
2021 | OriginalPaper | Buchkapitel
12. Ordinary Differential Equations
verfasst von : Tobias Weinzierl
Erschienen in: Principles of Parallel Scientific Computing
Abstract
There is a lot of definitions, terminology and theory around ordinary differential equations (ODEs). We introduce the terminology and properties that we need for our programming as well as the knowledge that we can exploit when we debug and assess codes. With the skills to rewrite any ODE into a system of first-order ODEs and the Taylor expansion, we finally have the mathematical tools to derive our explicit Euler formally. This chapter revisits some very basic properties of ordinary differential equations (ODEs). Feel free to skip the majority of this chapter and jump straight into Sect. 12.3, where we bring our ODE knowledge and the ideas behind Taylor together.