Continuous extensions of Rosenbrock-type methods
Solving the initial value problem for ordinary differential equations by a one-step method gives, in general, only discrete approximations at the grid points. For various applications these discrete values are not sufficient. One should have instead a so-called dense output (continuous extension): a numerical solution defined for each x belonging to the interval of integration. This paper deals with the construction of continuous extensions for Rosenbrock methods. Existence theorems - with no extra states - are proved. The extension for differential-algebraic equations is also considered. A numerical example for differential-algebraic equations illustrates the relevancy of the theory for practical computation.
scientific article; zbMATH DE number 4143366
scientific article