Efficient numerical integrators for stochastic models |
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| Institution: | 1. Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon street, WC1H 0AJ, London, UK;2. Departamento de Física Fundamental, UNED, Apartado 60141, 28080 Madrid, Spain;1. Departamento de Electrónica y Tecnología de Computadores, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain;2. Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain;3. Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain;1. KEK Theory Center, IPNS, KEK, Tsukuba, Ibaraki 305-0801, Japan;2. The Graduate University of Advanced Studies (Sokendai), Tsukuba, Ibaraki 305-0801, Japan;3. Kavli IPMU (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan;4. Department of Physics, University of Tokyo, Tokyo 113-0033, Japan;5. Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa 277-8582, Japan;1. Department of Physics, Faculty of Sciences(V), Lebanese University, Nabatieh, Lebanon;2. Institut de Physique, Université de Strasbourg, 3, rue de l׳Université, 67084 Strasbourg Cedex, France |
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| Abstract: | The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability. |
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