The order of numerical methods for ordinary differential equations

Author:
J. C. Butcher

Journal:
Math. Comp. **27** (1973), 793-806

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1973-0343620-7

MathSciNet review:
0343620

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0343620-7

Keywords:
Initial-value problems,
multistep methods,
Runge-Kutta methods,
order,
convergence

Article copyright:
© Copyright 1973
American Mathematical Society