1. On the Splitting Method for Some Complex-Valued Quasilinear Evolution Equations
- Author
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Annie Millet, Zdzisław Brzeźniak, Department of Mathematics, University of York, University of York [York, UK], Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM), Université Paris 1 Panthéon-Sorbonne (UP1), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and Springer
- Subjects
discretization scheme ,Independent equation ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Complex valued ,Schrödinger equation ,010103 numerical & computational mathematics ,16. Peace & justice ,01 natural sciences ,Euler equations ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Stochastic partial differential equation ,Sobolev space ,symbols.namesake ,MCS classification: Primary 60H15, 65M12 ,Secondary 65M60, 65M15 ,Simultaneous equations ,splitting method ,speed of convergence ,Convergence (routing) ,symbols ,0101 mathematics ,Stochastic evolution equations ,Mathematics - Abstract
International audience; Using the approach of the splitting method developed by I. Gyöngy and N. Krylov for parabolic quasi linear equations, we study the speed of convergence for general complex-valued stochastic evolution equations. The approximation is given in general Sobolev spaces and the model considered here contains both the parabolic quasi-linear equations under some (non strict) stochastic parabolicity condition as well as linear Schrödinger equations
- Published
- 2012