Numerical methods for stochastic partial differential equations with multiple scales

[1]  H. L. Dryden,et al.  Investigations on the Theory of the Brownian Movement , 1957 .

[2]  Thomas G. Kurtz,et al.  A limit theorem for perturbed operator semigroups with applications to random evolutions , 1973 .

[3]  G. Papanicolaou.  Some probabilistic problems and methods in singular perturbations , 1976 .

[4]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[5]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[6]  Werner Horsthemke,et al.  Noise-induced transitions , 1984 .

[7]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[8]  Stéphane Zaleski,et al.  A stochastic model for the large scale dynamics of some fluctuating interfaces , 1989 .

[9]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[10]  K. Elworthy.  ERGODICITY FOR INFINITE DIMENSIONAL SYSTEMS (London Mathematical Society Lecture Note Series 229) By G. Da Prato and J. Zabczyk: 339 pp., £29.95, LMS Members' price £22.47, ISBN 0 521 57900 7 (Cambridge University Press, 1996). , 1997 .

[11]  E. M. Lifshitz,et al.  Course in Theoretical Physics , 2013 .

[12]  Jessica G. Gaines,et al.  Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations , 2001, Math. Comput..

[13]  Andrew J. Majda,et al.  A mathematical framework for stochastic climate models , 2001 .

[14]  Dirk Blömker,et al.  The stochastic Landau equation as an amplitude equation , 2001 .

[15]  Jacques Printems,et al.  On the discretization in time of parabolic stochastic partial differential equations , 2001, Monte Carlo Methods Appl..

[16]  R. Zwanzig.  Nonequilibrium statistical mechanics , 2001, Physics Subject Headings (PhySH).

[17]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[18]  Andrew M. Stuart,et al.  Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions , 2002 .

[19]  Eric Vanden-Eijnden,et al.  NUMERICAL TECHNIQUES FOR MULTI-SCALE DYNAMICAL SYSTEMS WITH STOCHASTIC EFFECTS ⁄ , 2003 .

[20]  Modulation Equations: Stochastic Bifurcation in Large Domains , 2004, math-ph/0408016.

[21]  G. Parisi.  Brownian motion , 2005, Nature.

[22]  E. Vanden-Eijnden,et al.  Analysis of multiscale methods for stochastic differential equations , 2005 .

[23]  E. Saar.  Multiscale Methods , 2006, astro-ph/0612370.

[24]  T. Kurtz,et al.  Stochastic equations in infinite dimensions , 2006 .

[25]  I. Gyongy,et al.  On Numerical Approximation of Stochastic Burgers' Equation , 2006 .

[26]  A. Stuart,et al.  ANALYSIS OF SPDES ARISING IN PATH SAMPLING PART II: THE NONLINEAR CASE , 2006, math/0601092.

[27]  A. Abdulle,et al.  Stabilized methods for stiff stochastic systems , 2007 .

[28]  René Lefever,et al.  Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology , 2007 .

[29]  Martin Hairer,et al.  Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities , 2007 .

[30]  Michael Griebel,et al.  Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications , 2007 .

[31]  Mark Freidlin,et al.  Averaging principle for a class of stochastic reaction–diffusion equations , 2008, 0805.0297.

[32]  Martin Hairer,et al.  Some Remarks on Stabilization by Additive Noise , 2008 .

[33]  E. Weinan,et al.  Effectiveness of implicit methods for stiff stochastic differential equations , 2008 .

[34]  Andrew J Majda,et al.  An applied mathematics perspective on stochastic modelling for climate , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[35]  Assyr Abdulle,et al.  S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations , 2008, SIAM J. Sci. Comput..

[36]  A. Abdulle,et al.  S-ROCK methods for stiff Ito SDEs , 2008 .

[37]  Jacob Fish,et al.  Multiscale Methods: Bridging the Scales in Science and Engineering , 2009 .

[38]  Di Liu.  Analysis of Multiscale Methods for Stochastic Dynamical Systems with Multiple Time Scales , 2010, Multiscale Model. Simul..

[39]  Xiaoliang Wan,et al.  Study of the noise-induced transition and the exploration of the phase space for the Kuramoto–Sivashinsky equation using the minimum action method , 2010 .

[40]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .

[41]  G A Pavliotis,et al.  Noise induced state transitions, intermittency, and universality in the noisy Kuramoto-Sivashinksy equation. , 2010, Physical review letters.