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|Title:||A mass-preserving splitting scheme for the stochastic Schrödinger equation with multiplicative noise|
stochastic Schrödinger equation
|Source:||Liu, J. (2013-10). A mass-preserving splitting scheme for the stochastic Schrödinger equation with multiplicative noise. IMA Journal of Numerical Analysis 33 (4) : 1469-1479. ScholarBank@NUS Repository. https://doi.org/imanum/drs051|
|Abstract:||We present a mass-preserving scheme for the stochastic nonlinear Schrödinger equation with multiplicative noise of Stratonovich type. It is a splitting scheme and we present an explicit formula for solving the sub-step related to the nonlinear part. The scheme is unconditionally stable in the L2 norm. For the linear stochastic Schrödinger equation, we prove that the scheme has a strong convergence rate in time equal to 1, which is not common for stochastic partial differential equations with noise depending on space and time. © The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.|
|Source Title:||IMA Journal of Numerical Analysis|
|Appears in Collections:||Staff Publications|
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