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Weak second order explicit exponential Runge–Kutta methods for stochastic differential equations
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Innsbruck university.ORCID iD: 0000-0001-6490-1957
2017 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, no 6, p. A2857-A2878Article in journal (Refereed) Published
Abstract [en]

We propose new explicit exponential Runge--Kutta methods for the weak approximation of solutions of stiff Itô stochastic differential equations (SDEs). We also consider the use of exponential Runge--Kutta methods in combination with splitting methods. These methods have weak order 2 for multidimensional, noncommutative SDEs with a semilinear drift term, whereas they are of order 2 or 3 for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order 2.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017. Vol. 39, no 6, p. A2857-A2878
Keywords [en]
explicit method, exponential integrator, splitting method, stiffness, noncommutative noise, Itô stochastic differential equation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-137915DOI: 10.1137/15M1041341ISI: 000418659900030OAI: oai:DiVA.org:umu-137915DiVA, id: diva2:1128869
Available from: 2017-07-31 Created: 2017-07-31 Last updated: 2018-06-09Bibliographically approved

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Cohen, David

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