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Ordinary Differential Equations

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Numerical Approximation of Ordinary Differential Problems

Part of the book series: UNITEXT ((UNITEXTMAT,volume 148))

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Abstract

In order to properly address the issue of numerically solving any mathematical problem, it is always extremely important to understand as much as possible the problem itself. Hence, this chapter focuses on some basic issues on initial value problems for ordinary differential equations and, in particular, on the well-posedness of the problem and the stability of solutions. Some aspects regarding specific classes of problems, like discontinuous ODEs, dissipative problems and Hamiltonian problems are also addressed. Of course, this chapter does not pursue the aim of being a comprehensive treatise on the theory of ODEs; rather, the results here presented are clearly meant to provide significant issues relevant for computational purposes.

In order to solve this differential equation you look at it until a solution occurs to you.

(George Polya, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, 1945)

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  1. Department of Information Engineering and Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Raffaele D’Ambrosio

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D’Ambrosio, R. (2023). Ordinary Differential Equations. In: Numerical Approximation of Ordinary Differential Problems . UNITEXT(), vol 148. Springer, Cham. https://doi.org/10.1007/978-3-031-31343-1_1

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