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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


MS-Stability Analysis of Predictor-Corrector Schemes for Stochastic Differential Equations

Discontinuity, Nonlinearity, and Complexity 7(4) (2018) 397--401 | DOI:10.5890/DNC.2018.12.004

R. Zeghdane, A. Tocino

Department of Mathematics, University of Bordj Bou Arreridj, Algeria

Department of Mathematics, University of Salamanca, Spain

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Abstract

Deterministic predictor-corrector schemes are used mainly because of their numerical stability which they inherit from implicit counterparts of their corrector schemes. In principle these advantages carry over to the stochastic case. In this paper a complete study for the linear MS-stability of the oneparameter family of weak order 1.0 predictor-corrector Taylor schemes for scalar stochastic differential equations is given. Figures of the MS-stability regions that confirm the theoretical results are shown. It is also shown that mean- square A-stability is recovered if the parameter is increased.

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