The Cauchy Problem for Ordinary Differential Equations
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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.
KeywordsCauchy Problem Kutta Method Euler Method Integration Step Implicit Scheme
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