Abstract
We consider in this chapter the Cauchy problem for a system of ordinary differential equations (ODE). Under certain conditions the solution of this problem is a smooth integral curve in the space of unknowns and parameter, i.e., a one — parametric set similar to those considered at the previous chapter. This allows us to consider the Cauchy problem within the framework of the method of parametric continuation. Such a view leads to the formulation of the best continuation parameter problem, which is solved below.
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© 2003 Springer Science+Business Media Dordrecht
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Shalashilin, V.I., Kuznetsov, E.B. (2003). The Cauchy Problem for Ordinary Differential Equations. In: Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2537-8_2
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DOI: https://doi.org/10.1007/978-94-017-2537-8_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6391-5
Online ISBN: 978-94-017-2537-8
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