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Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stability properties of the drift-diagonally-implicit methods previously introduced (Debrabant and Rößler, Appl. Numer. Math. 59(3–4):595–607, 2009).
0006-3835
Abdulle, A.
d7c411ff-0a49-4ffb-91db-30710de5e860
Vilmart, G.
71ec2385-f222-46ec-85ea-8b33c4a0c205
Zygalakis, K.C.
a330d719-2ccb-49bd-8cd8-d06b1e6daca6
Abdulle, A.
d7c411ff-0a49-4ffb-91db-30710de5e860
Vilmart, G.
71ec2385-f222-46ec-85ea-8b33c4a0c205
Zygalakis, K.C.
a330d719-2ccb-49bd-8cd8-d06b1e6daca6

Abdulle, A., Vilmart, G. and Zygalakis, K.C. (2013) Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Bit Numerical Mathematics. (doi:10.1007/s10543-013-0430-8).

Record type: Article

Abstract

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stability properties of the drift-diagonally-implicit methods previously introduced (Debrabant and Rößler, Appl. Numer. Math. 59(3–4):595–607, 2009).

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e-pub ahead of print date: June 2013
Organisations: Applied Mathematics

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Local EPrints ID: 355729
URI: https://eprints.soton.ac.uk/id/eprint/355729
ISSN: 0006-3835
PURE UUID: 6ad25f37-99ff-4c81-93a3-4549763b68a7

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Date deposited: 04 Sep 2013 11:51
Last modified: 16 Jul 2019 21:26

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Contributors

Author: A. Abdulle
Author: G. Vilmart
Author: K.C. Zygalakis

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