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Volumn 82, Issue 9, 2012, Pages 1630-1644

Spectral collocation method for stochastic Burgers equation driven by additive noise

Author keywords

Spectral collocation method; Stochastic ordinary differential equation; Stochastic partial differential equation; System of SODEs

Indexed keywords

BURGERS EQUATIONS; COLLOCATION METHOD; CONVECTION EFFECTS; CONVERGENCE RATES; DIFFUSION TRANSPORT; FOURIER COLLOCATION METHOD; NUMERICAL EXPERIMENTS; REACTION MECHANISM; SPECTRAL COLLOCATION METHOD; STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS; STOCHASTIC PARTIAL DIFFERENTIAL EQUATION; SYSTEM OF SODES;

EID: 84861611189     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2012.03.007     Document Type: Article
Times cited : (26)

References (33)
  • 2
    • 46249084133 scopus 로고    scopus 로고
    • On modified Crank-Nicholson difference schemes for stochastic parabolic equation
    • A. Ashyralyev On modified Crank-Nicholson difference schemes for stochastic parabolic equation Numerical Functional Analysis and Optimization 29 3-4 2008 268 282
    • (2008) Numerical Functional Analysis and Optimization , vol.29 , Issue.34 , pp. 268-282
    • Ashyralyev, A.1
  • 4
    • 0001939954 scopus 로고
    • Stochastic partial differential equations in continuum physics on the foundations of the stochastic interpolation methods for It o ̂ type equations
    • N. Bellomo, and F. Flandoli Stochastic partial differential equations in continuum physics on the foundations of the stochastic interpolation methods for It o ̂ type equations Mathematics and Computers in Simulation 31 1989 3 17
    • (1989) Mathematics and Computers in Simulation , vol.31 , pp. 3-17
    • Bellomo, N.1    Flandoli, F.2
  • 6
    • 0031489544 scopus 로고    scopus 로고
    • The market model of interest rate dynamics
    • A. Brace, D. Gatarak, and M. Musiela The market model of interest rate dynamics Mathematical Finance 7 2 1997 127 147
    • (1997) Mathematical Finance , vol.7 , Issue.2 , pp. 127-147
    • Brace, A.1    Gatarak, D.2    Musiela, M.3
  • 9
    • 85011514513 scopus 로고    scopus 로고
    • Monte Carlo and Quasi-Monte Carlo methods
    • R.E. Caflisch Monte Carlo and Quasi-Monte Carlo methods Acta Numerica 1998 1 49
    • (1998) Acta Numerica , pp. 1-49
    • Caflisch, R.E.1
  • 13
    • 0039403112 scopus 로고
    • Existence and uniqueness results for semilinear stochastic partial differential equations
    • I. Gyöngy Existence and uniqueness results for semilinear stochastic partial differential equations Stochastic Processes and Their Applications 73 1988 271 299
    • (1988) Stochastic Processes and Their Applications , vol.73 , pp. 271-299
    • Gyöngy, I.1
  • 14
    • 55549131924 scopus 로고    scopus 로고
    • Finite element approximation of stochastic partial differential equations driven by Poisson random measures of jump type
    • E. Hausenblas Finite element approximation of stochastic partial differential equations driven by Poisson random measures of jump type SIAM Journal on Numerical Analysis 46 1 2007 437 471
    • (2007) SIAM Journal on Numerical Analysis , vol.46 , Issue.1 , pp. 437-471
    • Hausenblas, E.1
  • 15
    • 0037209607 scopus 로고    scopus 로고
    • Approximation for semilinear stochastic evolution equations
    • E. Hausenblas Approximation for semilinear stochastic evolution equations Potential Analysis 18 2003 141 186
    • (2003) Potential Analysis , vol.18 , pp. 141-186
    • Hausenblas, E.1
  • 16
    • 0037107474 scopus 로고    scopus 로고
    • Numerical analysis of semilinear stochastic evolution equations in Banach spaces
    • E. Hausenblas Numerical analysis of semilinear stochastic evolution equations in Banach spaces Journal of Computational and Applied Mathematics 147 2 2002 485 516
    • (2002) Journal of Computational and Applied Mathematics , vol.147 , Issue.2 , pp. 485-516
    • Hausenblas, E.1
  • 17
    • 33744543472 scopus 로고    scopus 로고
    • Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
    • T.Y. Hou, W. Luo, B. Rozovski, and H.M. Zhou Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics Journal of Computational Physics 216 2006 687 706
    • (2006) Journal of Computational Physics , vol.216 , pp. 687-706
    • Hou, T.Y.1    Luo, W.2    Rozovski, B.3    Zhou, H.M.4
  • 18
    • 70350393847 scopus 로고    scopus 로고
    • Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients
    • A. Jentzen Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients Potential Analysis 31 2009 375 404
    • (2009) Potential Analysis , vol.31 , pp. 375-404
    • Jentzen, A.1
  • 19
    • 58149125901 scopus 로고    scopus 로고
    • Overcoming the order barrier in the numerical approximation of SPDEs with additive space-time noise
    • A. Jentzen, and P.E. Kloeden Overcoming the order barrier in the numerical approximation of SPDEs with additive space-time noise. Proceedings of the Royal Society A 465 2102 2009 649 667
    • (2009) Proceedings of the Royal Society A , vol.465 , Issue.2102 , pp. 649-667
    • Jentzen, A.1    Kloeden, P.E.2
  • 20
    • 77950864660 scopus 로고    scopus 로고
    • The role of coefficients of a general SPDE on the stability and convergence of a finite difference method
    • M. Kamrani, and S.M. Hosseini The role of coefficients of a general SPDE on the stability and convergence of a finite difference method Journal of Computational and Applied Mathematics 234 2010 1426 1434
    • (2010) Journal of Computational and Applied Mathematics , vol.234 , pp. 1426-1434
    • Kamrani, M.1    Hosseini, S.M.2
  • 22
    • 0012150629 scopus 로고    scopus 로고
    • Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs
    • Special issue: Advances in Applied Stochastics
    • P.E. Kloeden, and S. Shott Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs Journal of Applied Mathematics and Stochastic Analysis 14 1 2001 47 53 Special issue: Advances in Applied Stochastics
    • (2001) Journal of Applied Mathematics and Stochastic Analysis , vol.14 , Issue.1 , pp. 47-53
    • Kloeden, P.E.1    Shott, S.2
  • 24
    • 34248191998 scopus 로고    scopus 로고
    • Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise
    • D. Liu Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise Communications in Mathematical Science 1 2 2003 361 375
    • (2003) Communications in Mathematical Science , vol.1 , Issue.2 , pp. 361-375
    • Liu, D.1
  • 25
    • 42649137906 scopus 로고    scopus 로고
    • Post processing for stochastic parabolic partial differential equations
    • G.J. Lord, and T. Shardlow Post processing for stochastic parabolic partial differential equations SIAM Journal on Numerical Analysis 45 2 2007 870 889
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , Issue.2 , pp. 870-889
    • Lord, G.J.1    Shardlow, T.2
  • 26
    • 0038906013 scopus 로고    scopus 로고
    • Numerical simulation of randomly forced turbulent flows
    • L. Machiels, and M.O. Deville Numerical simulation of randomly forced turbulent flows Journal of Computational Physics 145 1998 246 279
    • (1998) Journal of Computational Physics , vol.145 , pp. 246-279
    • MacHiels, L.1    Deville, M.O.2
  • 29
    • 34250880991 scopus 로고    scopus 로고
    • An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise
    • T. Muller-Gronbach, and K. Ritter An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise BIT 47 2 2007 393 418
    • (2007) BIT , vol.47 , Issue.2 , pp. 393-418
    • Muller-Gronbach, T.1    Ritter, K.2
  • 30
    • 85011454437 scopus 로고    scopus 로고
    • An introduction to numerical methods for stochastic differential equations
    • E. Platen An introduction to numerical methods for stochastic differential equations Acta Numerica 1999 197 246
    • (1999) Acta Numerica , pp. 197-246
    • Platen, E.1
  • 31
    • 30444440733 scopus 로고    scopus 로고
    • A Combination of Finite Difference and Wong-Zakai Methods for Hyperbolic Stochastic Partial Differential Equations
    • Ch. Roth A Combination of Finite Difference and Wong-Zakai Methods for Hyperbolic Stochastic Partial Differential Equations Stochastic Analysis and Applications 24 2006 221 240
    • (2006) Stochastic Analysis and Applications , vol.24 , pp. 221-240
    • Roth, Ch.1
  • 32
    • 21244455730 scopus 로고    scopus 로고
    • Finite Element Methods for Parabolic Stochastic PDE's
    • J.B. Walsh Finite Element Methods for Parabolic Stochastic PDE's Potential Analysis 23 2005 1 43
    • (2005) Potential Analysis , vol.23 , pp. 1-43
    • Walsh, J.B.1
  • 33
    • 33747184742 scopus 로고    scopus 로고
    • Galerkin finite element methods for stochastic parabolic partial differential equations
    • Y. Yan Galerkin finite element methods for stochastic parabolic partial differential equations SIAM Journal on Numerical Analysis 43 2005 1363 1384
    • (2005) SIAM Journal on Numerical Analysis , vol.43 , pp. 1363-1384
    • Yan, Y.1


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