Variable stepsize Runge-Kutta methods for stochastic wave equations

Details Variable stepsize Runge-Kutta methods for stochastic wave equations Variable stepsize Runge-Kutta methods for stochastic wave equations

2004-06-14

arxiv.org/abs/quant-ph/0406092v1

Physics Letters A, Volume 337, Issue 3, 4 April 2005, Pages 166-182

Physics

Quantum Physics

5 figures

Scientific paper

We show that existing Runge-Kutta methods for ordinary differential equations (odes) can be modified to solve stochastic differential equations (sdes) with strong solutions provided that appropriate changes are made to the way stepsizes are selected. The order of the resulting sde scheme is half the order of the ode scheme. Specifically, we show that an explicit 9th order Runge-Kutta method (with an embedded 8th order method) for odes yields an order 4.5 method for sdes which can be implemented with variable stepsizes. This method is tested by solving systems of sdes originating from stochastic wave equations arising from master equations and the many-body Schroedinger equation.

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