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The Cauchy Problem for Ordinary Differential Equations

  • V. I. Shalashilin
  • E. B. Kuznetsov
Chapter
  • 172 Downloads

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • V. I. Shalashilin
    • 1
  • E. B. Kuznetsov
    • 1
  1. 1.Moscow Aviation InstituteMoscowRussia

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