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Mathematics of Computation

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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: 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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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