Zhang, Shan; Guan, Xiaofei; Jiang, Lijian Convergence analysis of constraint energy minimizing generalized multiscale finite element method for a linear stochastic parabolic partial differential equation driven by additive noises. (English) Zbl 07309598 J. Comput. Appl. Math. 389, Article ID 113328, 18 p. (2021). MSC: 65 PDF BibTeX XML Cite \textit{S. Zhang} et al., J. Comput. Appl. Math. 389, Article ID 113328, 18 p. (2021; Zbl 07309598) Full Text: DOI
Izadpanah, Komeil; Mesforush, Ali; Nazemi, Ali Stabilized IMLS based element free Galerkin method for stochastic elliptic partial differential equations. (English) Zbl 1449.65316 J. Math. Model. 7, No. 4, 469-496 (2019). MSC: 65N30 93E24 60H40 35J15 35R60 PDF BibTeX XML Cite \textit{K. Izadpanah} et al., J. Math. Model. 7, No. 4, 469--496 (2019; Zbl 1449.65316) Full Text: DOI
Kuznetsov, Dmitriĭ Feliksovich Application of the method of approximation of iterated stochastic Itô integrals based on generalized multiple Fourier series to the high-order strong numerical methods for non-commutative semilinear stochastic partial differential equations. (English) Zbl 1433.60077 Differ. Uravn. Protsessy Upr. 2019, No. 3, 19-62 (2019). MSC: 60H35 60H05 65C30 60H15 PDF BibTeX XML Cite \textit{D. F. Kuznetsov}, Differ. Uravn. Protsessy Upr. 2019, No. 3, 19--62 (2019; Zbl 1433.60077) Full Text: Link
Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael A mild Itô formula for SPDEs. (English) Zbl 1423.35472 Trans. Am. Math. Soc. 372, No. 6, 3755-3807 (2019). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35R60 60H15 PDF BibTeX XML Cite \textit{G. Da Prato} et al., Trans. Am. Math. Soc. 372, No. 6, 3755--3807 (2019; Zbl 1423.35472) Full Text: DOI
Gunzburger, Max; Li, Buyang; Wang, Jilu Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise. (English) Zbl 07037308 Numer. Math. 141, No. 4, 1043-1077 (2019). MSC: 65 PDF BibTeX XML Cite \textit{M. Gunzburger} et al., Numer. Math. 141, No. 4, 1043--1077 (2019; Zbl 07037308) Full Text: DOI arXiv
Kazashi, Yoshihito; Gia, Quoc T. Le A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere. (English) Zbl 06996235 J. Complexity 50, 43-65 (2019). MSC: 65 76 PDF BibTeX XML Cite \textit{Y. Kazashi} and \textit{Q. T. Le Gia}, J. Complexity 50, 43--65 (2019; Zbl 06996235) Full Text: DOI arXiv
Bao, Jianhai; Huang, Xing; Yuan, Chenggui New regularity of Kolmogorov equation and application on approximation of semi-linear SPDEs with Hölder continuous drifts. (English) Zbl 1401.60120 Commun. Pure Appl. Anal. 18, No. 1, 341-360 (2019). MSC: 60H15 35R60 65C30 PDF BibTeX XML Cite \textit{J. Bao} et al., Commun. Pure Appl. Anal. 18, No. 1, 341--360 (2019; Zbl 1401.60120) Full Text: DOI
Roozbahani, M. M.; Aminikhah, H.; Tahmasebi, M. Numerical multi-scaling method to solve the linear stochastic partial differential equations. (English) Zbl 1402.60080 Comput. Appl. Math. 37, No. 4, 5527-5541 (2018). MSC: 60H15 60H35 65D07 65T60 PDF BibTeX XML Cite \textit{M. M. Roozbahani} et al., Comput. Appl. Math. 37, No. 4, 5527--5541 (2018; Zbl 1402.60080) Full Text: DOI
Baccouch, Mahboub A stochastic local discontinuous Galerkin method for stochastic two-point boundary-value problems driven by additive noises. (English) Zbl 1395.65070 Appl. Numer. Math. 128, 43-64 (2018). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 65M60 65L10 60H10 65L70 PDF BibTeX XML Cite \textit{M. Baccouch}, Appl. Numer. Math. 128, 43--64 (2018; Zbl 1395.65070) Full Text: DOI
Kamrani, Minoo; Blömker, Dirk Pathwise convergence of a numerical method for stochastic partial differential equations with correlated noise and local Lipschitz condition. (English) Zbl 1364.60088 J. Comput. Appl. Math. 323, 123-135 (2017). MSC: 60H35 60H15 60H10 65M12 65M60 PDF BibTeX XML Cite \textit{M. Kamrani} and \textit{D. Blömker}, J. Comput. Appl. Math. 323, 123--135 (2017; Zbl 1364.60088) Full Text: DOI
Wang, Yanqing A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations. (English) Zbl 1349.65493 Math. Control Relat. Fields 6, No. 3, 489-515 (2016). MSC: 65M60 65C30 60H35 60H15 60H10 PDF BibTeX XML Cite \textit{Y. Wang}, Math. Control Relat. Fields 6, No. 3, 489--515 (2016; Zbl 1349.65493) Full Text: DOI arXiv
Sauer, Martin; Stannat, Wilhelm Analysis and approximation of stochastic nerve axon equations. (English) Zbl 1342.60100 Math. Comput. 85, No. 301, 2457-2481 (2016). MSC: 60H15 60H35 35R60 65C30 92C20 PDF BibTeX XML Cite \textit{M. Sauer} and \textit{W. Stannat}, Math. Comput. 85, No. 301, 2457--2481 (2016; Zbl 1342.60100) Full Text: DOI
Dehghan, Mehdi; Shirzadi, Mohammad A meshless method based on the dual reciprocity method for one-dimensional stochastic partial differential equations. (English) Zbl 1337.65010 Numer. Methods Partial Differ. Equations 32, No. 1, 292-306 (2016). MSC: 65C30 60H15 60H35 35R60 65M38 PDF BibTeX XML Cite \textit{M. Dehghan} and \textit{M. Shirzadi}, Numer. Methods Partial Differ. Equations 32, No. 1, 292--306 (2016; Zbl 1337.65010) Full Text: DOI
Dehghan, Mehdi; Shirzadi, Mohammad Meshless simulation of stochastic advection-diffusion equations based on radial basis functions. (English) Zbl 1403.65086 Eng. Anal. Bound. Elem. 53, 18-26 (2015). MSC: 65M70 65M75 65C30 35R60 PDF BibTeX XML Cite \textit{M. Dehghan} and \textit{M. Shirzadi}, Eng. Anal. Bound. Elem. 53, 18--26 (2015; Zbl 1403.65086) Full Text: DOI
Jentzen, Arnulf; Röckner, Michael A Milstein scheme for SPDEs. (English) Zbl 1318.60072 Found. Comput. Math. 15, No. 2, 313-362 (2015). MSC: 60H35 60H15 65C30 PDF BibTeX XML Cite \textit{A. Jentzen} and \textit{M. Röckner}, Found. Comput. Math. 15, No. 2, 313--362 (2015; Zbl 1318.60072) Full Text: DOI arXiv
Sauer, Martin; Stannat, Wilhelm Lattice approximation for stochastic reaction diffusion equations with one-sided Lipschitz condition. (English) Zbl 1337.60162 Math. Comput. 84, No. 292, 743-766 (2015). MSC: 60H35 60H15 35R60 65C30 92C20 PDF BibTeX XML Cite \textit{M. Sauer} and \textit{W. Stannat}, Math. Comput. 84, No. 292, 743--766 (2015; Zbl 1337.60162) Full Text: DOI arXiv
Ghayebi, B.; Hosseini, S. M. A simplified milstein scheme for SPDEs with multiplicative noise. (English) Zbl 07021796 Abstr. Appl. Anal. 2014, Article ID 140849, 15 p. (2014). MSC: 65 62 PDF BibTeX XML Cite \textit{B. Ghayebi} and \textit{S. M. Hosseini}, Abstr. Appl. Anal. 2014, Article ID 140849, 15 p. (2014; Zbl 07021796) Full Text: DOI
Shen, Yi; Li, Yan Stationary in distributions of numerical solutions for stochastic partial differential equations with Markovian switching. (English) Zbl 1279.60082 Abstr. Appl. Anal. 2013, Article ID 752953, 12 p. (2013). MSC: 60H15 60H35 35R11 PDF BibTeX XML Cite \textit{Y. Shen} and \textit{Y. Li}, Abstr. Appl. Anal. 2013, Article ID 752953, 12 p. (2013; Zbl 1279.60082) Full Text: DOI
Qi, Ruisheng; Yang, Xiaoyuan Weak convergence of finite element method for stochastic elastic equation driven by additive noise. (English) Zbl 1290.65007 J. Sci. Comput. 56, No. 3, 450-470 (2013). Reviewer: Kevin Burrage (Brisbane) MSC: 65C30 60H15 60H35 35R60 65M20 65M60 PDF BibTeX XML Cite \textit{R. Qi} and \textit{X. Yang}, J. Sci. Comput. 56, No. 3, 450--470 (2013; Zbl 1290.65007) Full Text: DOI
Wang, Xiaojie; Gan, Siqing A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise. (English) Zbl 1267.65007 Numer. Algorithms 62, No. 2, 193-223 (2013). Reviewer: Grigori N. Milstein (Yekaterinburg) MSC: 65C30 60H35 60H15 35R60 65L06 PDF BibTeX XML Cite \textit{X. Wang} and \textit{S. Gan}, Numer. Algorithms 62, No. 2, 193--223 (2013; Zbl 1267.65007) Full Text: DOI arXiv
Wang, Xiaojie; Gan, Siqing Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise. (English) Zbl 1260.65006 J. Math. Anal. Appl. 398, No. 1, 151-169 (2013). Reviewer: Henri Schurz (Carbondale) MSC: 65C30 60H15 60H35 65M20 35R60 35L60 PDF BibTeX XML Cite \textit{X. Wang} and \textit{S. Gan}, J. Math. Anal. Appl. 398, No. 1, 151--169 (2013; Zbl 1260.65006) Full Text: DOI
Ashyralyev, Allaberen; San, Mehmet Emin An approximation of semigroups method for stochastic parabolic equations. (English) Zbl 1259.65003 Abstr. Appl. Anal. 2012, Article ID 684248, 24 p. (2012). MSC: 65C30 60H15 60H35 35R60 35K10 65M12 PDF BibTeX XML Cite \textit{A. Ashyralyev} and \textit{M. E. San}, Abstr. Appl. Anal. 2012, Article ID 684248, 24 p. (2012; Zbl 1259.65003) Full Text: DOI
Adamu, I. A.; Lord, G. J. Numerical approximation of multiplicative SPDEs. (English) Zbl 1258.35212 Int. J. Comput. Math. 89, No. 18, 2603-2621 (2012). MSC: 35R60 60H15 60H35 65M15 65M60 PDF BibTeX XML Cite \textit{I. A. Adamu} and \textit{G. J. Lord}, Int. J. Comput. Math. 89, No. 18, 2603--2621 (2012; Zbl 1258.35212) Full Text: DOI
Chong, Yuxiang; Walsh, John B. The roughness and smoothness of numerical solutions to the stochastic heat equation. (English) Zbl 1266.60114 Potential Anal. 37, No. 4, 303-332 (2012). Reviewer: Martin Ondreját (Praha) MSC: 60H15 35R60 60H35 65C30 PDF BibTeX XML Cite \textit{Y. Chong} and \textit{J. B. Walsh}, Potential Anal. 37, No. 4, 303--332 (2012; Zbl 1266.60114) Full Text: DOI
Aggez, Necmettin; Ashyralyyewa, Maral Numerical solution of stochastic hyperbolic equations. (English) Zbl 1246.65009 Abstr. Appl. Anal. 2012, Article ID 824819, 20 p. (2012). MSC: 65C30 60H15 65N06 PDF BibTeX XML Cite \textit{N. Aggez} and \textit{M. Ashyralyyewa}, Abstr. Appl. Anal. 2012, Article ID 824819, 20 p. (2012; Zbl 1246.65009) Full Text: DOI
Ryser, Marc D.; Nigam, Nilima; Tupper, Paul F. On the well-posedness of the stochastic Allen-Cahn equation in two dimensions. (English) Zbl 1242.65013 J. Comput. Phys. 231, No. 6, 2537-2550 (2012). MSC: 65C30 60H15 60H35 35R60 35Q35 PDF BibTeX XML Cite \textit{M. D. Ryser} et al., J. Comput. Phys. 231, No. 6, 2537--2550 (2012; Zbl 1242.65013) Full Text: DOI arXiv
Xu, Shengqiang; Duan, Jinqiao A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions. (English) Zbl 1220.65007 Appl. Math. Comput. 217, No. 23, 9532-9542 (2011). MSC: 65C30 60H15 35R60 35C10 35Q56 60H35 35Q40 PDF BibTeX XML Cite \textit{S. Xu} and \textit{J. Duan}, Appl. Math. Comput. 217, No. 23, 9532--9542 (2011; Zbl 1220.65007) Full Text: DOI
Kovács, Mihály; Lindgren, Fredrik; Larsson, Stig Spatial approximation of stochastic convolutions. (English) Zbl 1229.65027 J. Comput. Appl. Math. 235, No. 12, 3554-3570 (2011). Reviewer: Kevin Burrage (Brisbane) MSC: 65C30 65M60 65T60 60H15 60H35 PDF BibTeX XML Cite \textit{M. Kovács} et al., J. Comput. Appl. Math. 235, No. 12, 3554--3570 (2011; Zbl 1229.65027) Full Text: DOI
Debussche, Arnaud Weak approximation of stochastic partial differential equations: the nonlinear case. (English) Zbl 1217.65011 Math. Comput. 80, No. 273, 89-117 (2011). Reviewer: Gong Guanglu (Beijing) MSC: 65C30 65M15 60H15 60H35 35R60 65M06 60H07 PDF BibTeX XML Cite \textit{A. Debussche}, Math. Comput. 80, No. 273, 89--117 (2011; Zbl 1217.65011) Full Text: DOI
Hausenblas, Erika Weak approximation of the stochastic wave equation. (English) Zbl 1208.65016 J. Comput. Appl. Math. 235, No. 1, 33-58 (2010). Reviewer: Gong Guanglu (Beijing) MSC: 65C30 60H15 60H35 35R60 35L05 PDF BibTeX XML Cite \textit{E. Hausenblas}, J. Comput. Appl. Math. 235, No. 1, 33--58 (2010; Zbl 1208.65016) Full Text: DOI
Jentzen, Arnulf; Kloeden, Peter Taylor expansions of solutions of stochastic partial differential equations with additive noise. (English) Zbl 1220.35202 Ann. Probab. 38, No. 2, 532-569 (2010). Reviewer: Maria Christina Mariani (El Paso) MSC: 35R60 35K90 41A58 60H15 65C30 65M99 PDF BibTeX XML Cite \textit{A. Jentzen} and \textit{P. Kloeden}, Ann. Probab. 38, No. 2, 532--569 (2010; Zbl 1220.35202) Full Text: DOI arXiv
Jentzen, A.; Kloeden, P. E. The numerical approximation of stochastic partial differential equations. (English) Zbl 1205.60130 Milan J. Math. 77, 205-244 (2009). MSC: 60H35 60H15 35R60 65C30 PDF BibTeX XML Cite \textit{A. Jentzen} and \textit{P. E. Kloeden}, Milan J. Math. 77, 205--244 (2009; Zbl 1205.60130) Full Text: DOI
Debussche, Arnaud; Printems, Jacques Weak order for the discretization of the stochastic heat equation. (English) Zbl 1215.60043 Math. Comput. 78, No. 266, 845-863 (2009). Reviewer: Martin Riedler (Wien) MSC: 60H15 60H35 65C30 PDF BibTeX XML Cite \textit{A. Debussche} and \textit{J. Printems}, Math. Comput. 78, No. 266, 845--863 (2009; Zbl 1215.60043) Full Text: DOI
Jentzen, Arnulf; Kloeden, Peter E. Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. (English) Zbl 1186.65011 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2102, 649-667 (2009). MSC: 65C30 60H15 PDF BibTeX XML Cite \textit{A. Jentzen} and \textit{P. E. Kloeden}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2102, 649--667 (2009; Zbl 1186.65011) Full Text: DOI
Jentzen, Arnulf Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. (English) Zbl 1176.60051 Potential Anal. 31, No. 4, 375-404 (2009). MSC: 60H15 65C30 35K90 PDF BibTeX XML Cite \textit{A. Jentzen}, Potential Anal. 31, No. 4, 375--404 (2009; Zbl 1176.60051) Full Text: DOI
Ashyralyev, A. On modified Crank-Nicolson difference schemes for stochastic parabolic equation. (English) Zbl 1151.60033 Numer. Funct. Anal. Optim. 29, No. 3-4, 268-282 (2008). Reviewer: Lluís Quer-Sardanyons (Bellaterra) MSC: 60H35 60H15 60J35 PDF BibTeX XML Cite \textit{A. Ashyralyev}, Numer. Funct. Anal. Optim. 29, No. 3--4, 268--282 (2008; Zbl 1151.60033) Full Text: DOI
Bessaih, H.; Schurz, H. Upper bounds on the rate of convergence of truncated stochastic infinite-dimensional differential systems with \(H\)-regular noise. (English) Zbl 1136.60042 J. Comput. Appl. Math. 208, No. 2, 354-361 (2007). Reviewer: Dirk Blömker (Augsburg) MSC: 60H15 34F05 35G25 37H10 37L65 60H35 60H25 PDF BibTeX XML Cite \textit{H. Bessaih} and \textit{H. Schurz}, J. Comput. Appl. Math. 208, No. 2, 354--361 (2007; Zbl 1136.60042) Full Text: DOI
Hausenblas, Erika; Marchis, Iuliana A numerical approximation of parabolic stochastic partial differential equations driven by a Poisson random measure. (English) Zbl 1112.65004 BIT 46, No. 4, 773-811 (2006). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 60H15 35R60 60H35 PDF BibTeX XML Cite \textit{E. Hausenblas} and \textit{I. Marchis}, BIT 46, No. 4, 773--811 (2006; Zbl 1112.65004) Full Text: DOI
Quer-Sardanyons, Lluís; Sanz-Solé, Marta Space semi-discretisations for a stochastic wave equation. (English) Zbl 1119.60061 Potential Anal. 24, No. 4, 303-332 (2006). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H35 60H15 65C30 35R60 35L05 PDF BibTeX XML Cite \textit{L. Quer-Sardanyons} and \textit{M. Sanz-Solé}, Potential Anal. 24, No. 4, 303--332 (2006; Zbl 1119.60061) Full Text: DOI
Pettersson, Roger; Signahl, Mikael Numerical approximation for a white noise driven SPDE with locally bounded drift. (English) Zbl 1065.35221 Potential Anal. 22, No. 4, 375-393 (2005). MSC: 35R60 PDF BibTeX XML Cite \textit{R. Pettersson} and \textit{M. Signahl}, Potential Anal. 22, No. 4, 375--393 (2005; Zbl 1065.35221) Full Text: DOI
Shardlow, Tony Numerical simulation of stochastic PDEs for excitable media. (English) Zbl 1066.65017 J. Comput. Appl. Math. 175, No. 2, 429-446 (2005). Reviewer: Eckhard Platen (Broadway) MSC: 65C30 60H15 35K57 60H35 PDF BibTeX XML Cite \textit{T. Shardlow}, J. Comput. Appl. Math. 175, No. 2, 429--446 (2005; Zbl 1066.65017) Full Text: DOI
Hausenblas, Erika Numerical analysis of semilinear stochastic evolution equations in Banach spaces. (English) Zbl 1026.65005 J. Comput. Appl. Math. 147, No. 2, 485-516 (2002). Reviewer: Grigori Milstein (Berlin) MSC: 65C30 60H15 60H35 PDF BibTeX XML Cite \textit{E. Hausenblas}, J. Comput. Appl. Math. 147, No. 2, 485--516 (2002; Zbl 1026.65005) Full Text: DOI
Printems, Jacques On the discretization in time of parabolic stochastic partial differential equations. (English) Zbl 0991.60051 M2AN, Math. Model. Numer. Anal. 35, No. 6, 1055-1078 (2001). Reviewer: Eckhard Platen (Broadway) MSC: 60H15 60F25 65C20 PDF BibTeX XML Cite \textit{J. Printems}, M2AN, Math. Model. Numer. Anal. 35, No. 6, 1055--1078 (2001; Zbl 0991.60051) Full Text: DOI Numdam EuDML