On the convergence of multistep methods for the Cauchy problem for ordinary differential equations

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The general form of a quasilinear nonstationary k-step method for solving of the Cauchy problem for ordinary differential equations is discussed. The convergence theorem is stated under rather weak conditions. It is not assumed that the increment function is Lipschitz-continuous but only that it satisfies the Perron type condition appearing in the uniqueness theory for the Cauchy problem with a nondecreasing comparison function. The result established in the paper is an extension of the theory given by G. Dahlquist and the recent result of K. Taubert.

Original languageEnglish (US)
Pages (from-to)351-361
Number of pages11
JournalComputing
Volume20
Issue number4
DOIs
StatePublished - Dec 1978
Externally publishedYes

Fingerprint

Multistep Methods
Ordinary differential equations
Cauchy Problem
Ordinary differential equation
Convergence Theorem
Increment
Lipschitz
Uniqueness
Form

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

On the convergence of multistep methods for the Cauchy problem for ordinary differential equations. / Jackiewicz, Zdzislaw; Kwapisz, M.

In: Computing, Vol. 20, No. 4, 12.1978, p. 351-361.

Research output: Contribution to journalArticle

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