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Necessary conditions for the convergence of the generalized periodic overimplicit multistep method

Hassan Nasr Ahmed Ismail — 1979

Aplikace matematiky

This paper is the continuation of the paper "Generalized periodic overimplicit multistep methods" of the same author and it deals with the necessary and, in some special cases, with the necessary and sufficient conditions for the convergence of general periodic overimplicit multistep methods.

Generalized periodic overimplicit multistep methods (GPOM methods)

Hassan Nasr Ahmed Ismail — 1979

Aplikace matematiky

The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.

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