The order of numerical methods for ordinary differential equations

Butcher, J. C.

doi:10.1090/S0025-5718-1973-0343620-7

The order of numerical methods for ordinary differential equations
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Math. Comp. 27 (1973), 793-806 Request permission

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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