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Analysis of a Modified Regularity-Preserving Euler Scheme for Parabolic Semilinear SPDEs: Total Variation Error Bounds for the Numerical Approximation of the Invariant Distribution
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A splitting semi-implicit Euler method for stochastic incompressible Euler equations on 𝕋2
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Numerical conservation issues for the stochastic Korteweg–de Vries equation
Splitting schemes for FitzHugh–Nagumo stochastic partial differential equations
Charles-Edouard Bréhier, David Cohen and Giuseppe Giordano Discrete and Continuous Dynamical Systems - B (2023) https://doi.org/10.3934/dcdsb.2023094
Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise
K. Fahim, E. Hausenblas and M. Kovács Stochastics and Partial Differential Equations: Analysis and Computations 11(3) 1044 (2023) https://doi.org/10.1007/s40072-022-00250-0
Strong $$L^2$$ convergence of time Euler schemes for stochastic 3D Brinkman–Forchheimer–Navier–Stokes equations
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions
Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen, Jan van Neerven and Timo Welti IMA Journal of Numerical Analysis 41(1) 493 (2021) https://doi.org/10.1093/imanum/drz063
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities
Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise
Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise
Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method
Amaneh Sepahvandzadeh, Bahman Ghazanfari and Nader Asadian Mathematical and Computational Applications 23(4) 53 (2018) https://doi.org/10.3390/mca23040053
Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn--Hilliard Equation
Daisuke Furihata, Mihály Kovács, Stig Larsson and Fredrik Lindgren SIAM Journal on Numerical Analysis 56(2) 708 (2018) https://doi.org/10.1137/17M1121627
Optimal Strong Rates of Convergence for a Space-Time Discretization of
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Strong Convergence Analysis of the Stochastic Exponential Rosenbrock Scheme for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise
Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces
Hakima Bessaih, Erika Hausenblas, Tsiry Avisoa Randrianasolo and Paul André Razafimandimby Journal of Computational and Applied Mathematics 343 250 (2018) https://doi.org/10.1016/j.cam.2018.04.067
Implicit Euler method for numerical solution of nonlinear stochastic partial differential equations with multiplicative trace class noise
Minoo Kamrani, S. Mohammad Hosseini and Erika Hausenblas Mathematical Methods in the Applied Sciences 41(13) 4986 (2018) https://doi.org/10.1002/mma.4946
Numerical Methods for Stochastic Partial Differential Equations with White Noise
Zhongqiang Zhang and George Em Karniadakis Applied Mathematical Sciences, Numerical Methods for Stochastic Partial Differential Equations with White Noise 196 53 (2017) https://doi.org/10.1007/978-3-319-57511-7_3
Regularity of the Mild Solution of a Parabolic Equation with Stochastic Measure
Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
W. W. Mohammed, M. A. Sohaly, A. H. El-Bassiouny and K. A. Elnagar American Journal of Computational Mathematics 04(04) 280 (2014) https://doi.org/10.4236/ajcm.2014.44024
An Implicit Algorithm of Solving Nonlinear Filtering Problems
Splitting up method for the 2D stochastic Navier–Stokes equations
H. Bessaih, Z. Brzeźniak and A. Millet Stochastic Partial Differential Equations: Analysis and Computations 2(4) 433 (2014) https://doi.org/10.1007/s40072-014-0041-7
Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise
Mihály Kovács, Stig Larsson and Karsten Urban Springer Proceedings in Mathematics & Statistics, Monte Carlo and Quasi-Monte Carlo Methods 2012 65 481 (2013) https://doi.org/10.1007/978-3-642-41095-6_24
Nonconforming finite element method for stochastic Stokes equations
Zdzisław Brzeźniak and Annie Millet Springer Proceedings in Mathematics & Statistics, Stochastic Analysis and Related Topics 22 57 (2012) https://doi.org/10.1007/978-3-642-29982-7_3
Asymptotics for a generalized Cahn-Hilliard equation
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Dimitra Antonopoulou, Georgia Karali and Georgios T. Kossioris Discrete & Continuous Dynamical Systems - A 30(4) 1037 (2011) https://doi.org/10.3934/dcds.2011.30.1037
Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise
Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
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Finite Element Approximation of Stochastic Partial Differential Equations driven by Poisson Random Measures of Jump Type