The order of numerical methods for ordinary differential equations-Reference-Cited by-同舟云学术

The order of numerical methods for ordinary differential equations

Published:1973 Issue:124 Volume:27 Page:793-806
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Butcher J. C.

Abstract

For a general class of methods, which includes linear multistep and Runge-Kutta methods as special cases, a concept of order relative to a given starting procedure is defined and an order of convergence theorem is proved. The definition is given an algebraic interpretation and illustrated by the derivation of a particular fourth-order method.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1973-27-124/S0025-5718-1973-0343620-7/S0025-5718-1973-0343620-7.pdf

Reference12 articles.

1. Stability and error bounds in the numerical integration of ordinary differential equations;Dahlquist, Germund;Kungl. Tekn. H\"{o}gsk. Handl. Stockholm,1959

2. Theory of errors in numerical integration of ordinary differential equations;Urabe, Minoru;J. Sci. Hiroshima Univ. Ser. A-I Math.,1961

3. Approximate computation of errors in numerical integration of ordinary differential equations by one-step methods;Shintani, Hisayoshi;J. Sci. Hiroshima Univ. Ser. A-I Math.,1965

4. Periodic solutions of van der Pol’s equation with damping coefficient 𝜆=2∼10;Urabe, Minoru;J. Sci. Hiroshima Univ. Ser. A,1960

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