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| {equation, function, exp} |
| {state, algorithm, problem} |
| {measurement, state, measurements} |
| {time, wave, function} |
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Variable stepsize Runge-Kutta methods for stochastic wave equations
Joshua Wilkie, Murat Cetinbas
abstract: 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0406092
- categories:
- quant-ph
- comments:
- 5 figures
- arxiv_id:
- quant-ph/0406092
- journal_ref:
- Physics Letters A, Volume 337, Issue 3, 4 April 2005, Pages
166-182
- created:
- 2004-06-14
Full article ▸
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