The Cauchy Problem for Ordinary Differential Equations

V. I. Shalashilin and E. B. Kuznetsov
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V. I. Shalashilin: Moscow Aviation Institute
E. B. Kuznetsov: Moscow Aviation Institute

Chapter Chapter 2 in Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics, 2003, pp 43-66 from Springer

Abstract: 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.

Keywords: Cauchy Problem; Kutta Method; Euler Method; Integration Step; Implicit Scheme (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2537-8_2

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DOI: 10.1007/978-94-017-2537-8_2

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