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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Regular Runge-Kutta pairs

Higham, D.J. (1997) Regular Runge-Kutta pairs. Applied Numerical Mathematics, 25. pp. 229-241. ISSN 0168-9274

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Abstract

Time-stepping methods that guarantee to avoid spurious fixed points are said to be regular. For fixed stepsize Runge-Kutta formulas, this concept has been well studied. Here, the theory of regularity is extended to the case of embedded Runge-Kutta pairs used in variable stepsize mode with local error control. First, the limiting case of a zero error tolerance is considered. A recursive regularity test, based on the folding technique of Hairer, Iserles and Sanz-Serna (1990), is developed. It is then shown how regularity at zero tolerance carries through to the case of small tolerances. Finally, the property of regularity for all tolerances is characterized.