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- The Leimkuhler-Matthews method (or LM method in its original paper ) is an algorithm for finding discretized solutions to the Brownian dynamics where is a constant and can be thought of as a potential energy function commonly found in classical molecular dynamics, with the dimensional state vector along with dimensional Wiener process denoted . Given a time step , the Leimkuhler-Matthews update scheme is compactly written as with initial condition , and where is a vector of independent normal random numbers redrawn at each step so (where denotes expectation). Despite being of equal cost to the Euler-Maruyama scheme (in terms of the number of evaluations of the function per update), given some assumptions on and solutions have been shown to have a superconvergence property for constants not depending on . This means that as gets large we obtain an effective second order with error in computed expectations. For small time step this can give significant improvements over the Euler-Maruyama scheme, at no extra cost. (en)
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- 6482 (xsd:nonNegativeInteger)
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- The Leimkuhler-Matthews method (or LM method in its original paper ) is an algorithm for finding discretized solutions to the Brownian dynamics where is a constant and can be thought of as a potential energy function commonly found in classical molecular dynamics, with the dimensional state vector along with dimensional Wiener process denoted . Given a time step , the Leimkuhler-Matthews update scheme is compactly written as (en)
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- Leimkuhler–Matthews method (en)
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