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High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

✍ Scribed by K. Burrage; P.M. Burrage

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
915 KB
Volume
22
Category
Article
ISSN
0168-9274

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✦ Synopsis

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general Class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

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