Fetching the paper…
Reading the bibliography…
In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise.
Da Prato, G., and Zabczyk, J., Stochastic equations in infinite dimensions, vol. 44 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1992
1992
Earlier work this paper cites.
Kloeden, P.E., and Platen, E., Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992
1992
Earlier work this paper cites.
Burrage, K. and Burrage, P.M., High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Appl. Numer. Math., 22 (1996), 81-101
1996
Earlier work this paper cites.
Grecksch, W., and Kloeden, P.E., Time-discretised Galerkin approximations of parabolic stochastic PDEs. Bull. Austral. Math. Soc. 54, 1 (1996), 79-85
1996
Earlier work this paper cites.
Gyöngy, I., Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II. Potential Anal. 11, 1 (1999), 1-37
1999
Earlier work this paper cites.
Shardlow, T., Numerical methods for stochastic parabolic PDEs. Numer. Funct. Anal. Optim. 20, 1-2 (1999), 121-145
1999
Earlier work this paper cites.
Shardlow, T., Weak convergence of a numerical method for a stochastic heat equation. BIT, 43 (2003), 179-193
2003
Cited alongside, same era.
Lord, G.J., and Rougemont, J., A numerical scheme for stochastic PDEs with Gevrey regularity. IMA J. Numer. Anal. 24, 4 (2004), 587-604
2004
Cited alongside, same era.
Yan, Y., Galerkin finite element methods for stochastic parabolic partial differential equations. SIAM J. Numer. Anal. 43, 4 (2005), 1363-1384
2005
Cited alongside, same era.
Chow, P.L., Stochastic Partial Differential Equations. Chapman & \& Hall/CRC, New York, 2007
2007
Cited alongside, same era.
Prévôt, C., and Röckner, M., A concise course on stochastic partial differential equations, vol. 1905 of Lecture Notes in Mathematics. Springer, Berlin, 2007
2007
Cited alongside, same era.
Jentzen, A., and Kloeden, P.E., The numerical approximation of stochastic partial differential equations. Milan J. Math. 77, 1 (2009), 205-244
2009
Later among the works it cites.
Kovács, M., Larsson, S., and Lindgren, F., Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations with additive noise. Numer. Algor. 53 (2010) 309-320
2010
Later among the works it cites.
2010
Later among the works it cites.
Kloeden, P.E., Lord, G.J., Neuenkirch, A. and Shardlow, T., The exponential integrator scheme for stochastic partial differential equations: pathwise error bounds. J. Comput. Appl. Math. 235, 5 (2011), 1245-1260
2011
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Jentzen, A., and Kloeden, P.E., Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465, 2102 (2009), 649-667
2009
Cited alongside, same era.
Jentzen, A., and Röckner, M., Regularity analysis of stochastic partial differential equations with nonlinear multiplicative trace class noise. J. Differential Equations 252 (2012), no.1, 114-136
2012
Closest in time.