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Published in:
2018 | OriginalPaper | Chapter
21. Numerical Solution of Differential Equations
Authors : Michael Oberguggenberger, Alexander Ostermann
Published in: Analysis for Computer Scientists
Publisher: Springer International Publishing
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Abstract
As we have seen in the last two chapters, only particular classes of differential equations can be solved analytically. Especially for nonlinear problems one has to rely on numerical methods. In this chapter we discuss several variants of Euler’s method as a prototype. Motivated by the Taylor expansion of the analytical solution we deduce Euler approximations and study their stability properties. In this way we introduce the reader to several important aspects of the numerical solution of differential equations. We point out, however, that for most real-life applications one has to use more sophisticated numerical methods.