Block RungeKutta methods for the numerical integration of initial value problems in ordinary differential equations. I. The nonstiff case
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 by J. R. Cash PDF
 Math. Comp. 40 (1983), 175191 Request permission
Abstract:
Block RungeKutta formulae suitable for the approximate numerical integration of initial value problems for first order systems of ordinary differential equations are derived. Considered in detail are the problems of varying both order and stepsize automatically. This leads to a class of variable order block explicit RungeKutta formulae for the integration of nonstiff problems and a class of variable order block implicit formulae suitable for stiff problems. The central idea is similar to one due to C. W. Gear in developing RungeKutta starters for linear multistep methods. Some numerical results are given to illustrate the algorithms developed for both the stiff and nonstiff cases and comparisons with standard RungeKutta methods are made.References

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Additional Information
 © Copyright 1983 American Mathematical Society
 Journal: Math. Comp. 40 (1983), 175191
 MSC: Primary 65L05
 DOI: https://doi.org/10.1090/S00255718198306794393
 MathSciNet review: 679439