Tyranowski, Tomasz M. Data-driven structure-preserving model reduction for stochastic Hamiltonian systems. (English) Zbl 07815422 J. Comput. Dyn. 11, No. 2, 220-255 (2024). MSC: 65C30 65D30 PDFBibTeX XMLCite \textit{T. M. Tyranowski}, J. Comput. Dyn. 11, No. 2, 220--255 (2024; Zbl 07815422) Full Text: DOI arXiv
Anton, Cristina Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems. (English) Zbl 1524.65023 Appl. Numer. Math. 185, 18-37 (2023). MSC: 65C30 60H10 60H35 65L06 65P10 PDFBibTeX XMLCite \textit{C. Anton}, Appl. Numer. Math. 185, 18--37 (2023; Zbl 1524.65023) Full Text: DOI
Cordoni, Francesco Giuseppe; Di Persio, Luca; Muradore, Riccardo Discrete stochastic port-Hamiltonian systems. (English) Zbl 1482.93585 Automatica 137, Article ID 110122, 8 p. (2022). MSC: 93E03 93B70 PDFBibTeX XMLCite \textit{F. G. Cordoni} et al., Automatica 137, Article ID 110122, 8 p. (2022; Zbl 1482.93585) Full Text: DOI
D’Ambrosio, Raffaele; Scalone, Carmela Two-step Runge-Kutta methods for stochastic differential equations. (English) Zbl 1510.65013 Appl. Math. Comput. 403, Article ID 125930, 11 p. (2021). MSC: 65C30 60H10 65L06 PDFBibTeX XMLCite \textit{R. D'Ambrosio} and \textit{C. Scalone}, Appl. Math. Comput. 403, Article ID 125930, 11 p. (2021; Zbl 1510.65013) Full Text: DOI
Haghighi, A. New S-ROCK methods for stochastic differential equations with commutative noise. (English) Zbl 1522.65012 Iran. J. Numer. Anal. Optim. 9, No. 1, 105-126 (2019). MSC: 65C30 60H10 60H35 65L04 65L06 PDFBibTeX XMLCite \textit{A. Haghighi}, Iran. J. Numer. Anal. Optim. 9, No. 1, 105--126 (2019; Zbl 1522.65012) Full Text: DOI
Tang, Xiao; Xiao, Aiguo Asymptotically optimal approximation of some stochastic integrals and its applications to the strong second-order methods. (English) Zbl 1415.60057 Adv. Comput. Math. 45, No. 2, 813-846 (2019). MSC: 60H05 60H35 65C30 PDFBibTeX XMLCite \textit{X. Tang} and \textit{A. Xiao}, Adv. Comput. Math. 45, No. 2, 813--846 (2019; Zbl 1415.60057) Full Text: DOI
Gong, Chen Chris; Zheng, Chunming; Toenjes, Ralf; Pikovsky, Arkady Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise. (English) Zbl 1411.34063 Chaos 29, No. 3, 033127, 11 p. (2019). MSC: 34C60 34C15 34F05 PDFBibTeX XMLCite \textit{C. C. Gong} et al., Chaos 29, No. 3, 033127, 11 p. (2019; Zbl 1411.34063) Full Text: DOI arXiv
Gevorkyan, Migran N.; Demidova, Anastasiya V.; Korolkova, Anna V.; Kulyabov, Dmitry S. Issues in the software implementation of stochastic numerical Runge-Kutta. (English) Zbl 1477.65021 Vishnevskiy, Vladimir M. (ed.) et al., Distributed computer and communication networks. 21st international conference, DCCN 2018, Moscow, Russia, September 17–21, 2018. Proceedings. Cham: Springer. Commun. Comput. Inf. Sci. 919, 532-546 (2018). MSC: 65C30 60H35 65L06 PDFBibTeX XMLCite \textit{M. N. Gevorkyan} et al., Commun. Comput. Inf. Sci. 919, 532--546 (2018; Zbl 1477.65021) Full Text: DOI arXiv
Holm, Darryl D.; Tyranowski, Tomasz M. Stochastic discrete Hamiltonian variational integrators. (English) Zbl 06989587 BIT 58, No. 4, 1009-1048 (2018). MSC: 65C30 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{T. M. Tyranowski}, BIT 58, No. 4, 1009--1048 (2018; Zbl 06989587) Full Text: DOI arXiv
Wang, Bo; Qi, Qianqian Modeling the lake eutrophication stochastic ecosystem and the research of its stability. (English) Zbl 1392.92114 Math. Biosci. 300, 102-114 (2018). MSC: 92D40 PDFBibTeX XMLCite \textit{B. Wang} and \textit{Q. Qi}, Math. Biosci. 300, 102--114 (2018; Zbl 1392.92114) Full Text: DOI
Rackauckas, Christopher; Nie, Qing Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory. (English) Zbl 1366.65005 Discrete Contin. Dyn. Syst., Ser. B 22, No. 7, 2731-2761 (2017). MSC: 65C30 60H10 60H35 34F05 65L06 PDFBibTeX XMLCite \textit{C. Rackauckas} and \textit{Q. Nie}, Discrete Contin. Dyn. Syst., Ser. B 22, No. 7, 2731--2761 (2017; Zbl 1366.65005) Full Text: DOI
Bastani, Ali Foroush; Damircheli, Davood An adaptive algorithm for solving stochastic multi-point boundary value problems. (English) Zbl 1362.65009 Numer. Algorithms 74, No. 4, 1119-1143 (2017). MSC: 65C30 60H10 60H35 35F05 34B10 65L20 PDFBibTeX XMLCite \textit{A. F. Bastani} and \textit{D. Damircheli}, Numer. Algorithms 74, No. 4, 1119--1143 (2017; Zbl 1362.65009) Full Text: DOI arXiv
Xiao, Aiguo; Tang, Xiao High strong order stochastic Runge-Kutta methods for Stratonovich stochastic differential equations with scalar noise. (English) Zbl 1342.60116 Numer. Algorithms 72, No. 2, 259-296 (2016). MSC: 60H35 60H10 65C30 65L06 65L20 PDFBibTeX XMLCite \textit{A. Xiao} and \textit{X. Tang}, Numer. Algorithms 72, No. 2, 259--296 (2016; Zbl 1342.60116) Full Text: DOI
Haghighi, Amir; Hosseini, Seyed Mohammad; Rößler, Andreas Diagonally drift-implicit Runge-Kutta methods of strong order one for stiff stochastic differential systems. (English) Zbl 1329.65014 J. Comput. Appl. Math. 293, 82-93 (2016). MSC: 65C30 PDFBibTeX XMLCite \textit{A. Haghighi} et al., J. Comput. Appl. Math. 293, 82--93 (2016; Zbl 1329.65014) Full Text: DOI
Abdulle, Assyr Explicit methods for stiff stochastic differential equations. (English) Zbl 1246.65007 Engquist, Björn (ed.) et al., Numerical analysis of multiscale computations. Proceedings of a winter workshop at the Banff International Research Station 2009, Canada, December 6–11, 2011. Berlin: Springer (ISBN 978-3-642-21942-9/hbk; 978-3-642-21943-6/ebook). Lecture Notes in Computational Science and Engineering 82, 1-22 (2012). MSC: 65C30 60H15 60H35 35R60 65M20 65M06 65M12 PDFBibTeX XMLCite \textit{A. Abdulle}, Lect. Notes Comput. Sci. Eng. 82, 1--22 (2012; Zbl 1246.65007) Full Text: DOI Link
Debrabant, Kristian; Kværnø, Anne Composition of stochastic B-series with applications to implicit Taylor methods. (English) Zbl 1208.65014 Appl. Numer. Math. 61, No. 4, 501-511 (2011). MSC: 65C30 PDFBibTeX XMLCite \textit{K. Debrabant} and \textit{A. Kværnø}, Appl. Numer. Math. 61, No. 4, 501--511 (2011; Zbl 1208.65014) Full Text: DOI arXiv
Debrabant, Kristian; Kværnø, Anne Stochastic Taylor expansions: Weight functions of B-series expressed as multiple integrals. (English) Zbl 1188.65005 Stochastic Anal. Appl. 28, No. 2, 293-302 (2010). Reviewer: Kevin Burrage (Brisbane) MSC: 65C30 60H10 PDFBibTeX XMLCite \textit{K. Debrabant} and \textit{A. Kværnø}, Stochastic Anal. Appl. 28, No. 2, 293--302 (2010; Zbl 1188.65005) Full Text: DOI
Ninomiya, Mariko; Ninomiya, Syoiti A new higher-order weak approximation scheme for stochastic differential equations and the Runge-Kutta method. (English) Zbl 1199.65011 Finance Stoch. 13, No. 3, 415-443 (2009). Reviewer: Yuliya Mishura (Kyïv) MSC: 65C30 65C05 65L06 17B01 91G60 60H10 PDFBibTeX XMLCite \textit{M. Ninomiya} and \textit{S. Ninomiya}, Finance Stoch. 13, No. 3, 415--443 (2009; Zbl 1199.65011) Full Text: DOI arXiv
Omar, M. A.; Aboul-Hassan, A.; Rabia, S. I. The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations. (English) Zbl 1206.65024 Appl. Math. Comput. 215, No. 2, 727-745 (2009). Reviewer: Grigori N. Milstein (Ekaterinburg) MSC: 65C30 60H10 60H35 34F05 65L20 PDFBibTeX XMLCite \textit{M. A. Omar} et al., Appl. Math. Comput. 215, No. 2, 727--745 (2009; Zbl 1206.65024) Full Text: DOI
Komori, Yoshio Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations. (English) Zbl 1117.65010 J. Comput. Appl. Math. 206, No. 1, 158-173 (2007). MSC: 65C30 60H10 60H35 65L06 PDFBibTeX XMLCite \textit{Y. Komori}, J. Comput. Appl. Math. 206, No. 1, 158--173 (2007; Zbl 1117.65010) Full Text: DOI
Buckwar, Evelyn; Winkler, Renate Improved linear multi-step methods for stochastic ordinary differential equations. (English) Zbl 1128.65005 J. Comput. Appl. Math. 205, No. 2, 912-922 (2007). Reviewer: Jialin Hong (Beijing) MSC: 65C30 60H10 34F05 60H35 65L06 65L20 PDFBibTeX XMLCite \textit{E. Buckwar} and \textit{R. Winkler}, J. Comput. Appl. Math. 205, No. 2, 912--922 (2007; Zbl 1128.65005) Full Text: DOI
Komori, Yoshio Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations. (English) Zbl 1112.65005 J. Comput. Appl. Math. 203, No. 1, 57-79 (2007). MSC: 65C30 60H10 60H35 34F05 65L06 PDFBibTeX XMLCite \textit{Y. Komori}, J. Comput. Appl. Math. 203, No. 1, 57--79 (2007; Zbl 1112.65005) Full Text: DOI
Rößler, Andreas Runge-Kutta methods for Itô stochastic differential equations with scalar noise. (English) Zbl 1091.65004 BIT 46, No. 1, 97-110 (2006). MSC: 65C30 65L06 60H35 60H10 PDFBibTeX XMLCite \textit{A. Rößler}, BIT 46, No. 1, 97--110 (2006; Zbl 1091.65004) Full Text: DOI
Carbonell, F.; Jimenez, J. C.; Biscay, R. J. A class of orthogonal integrators for stochastic differential equations. (English) Zbl 1078.65004 J. Comput. Appl. Math. 182, No. 2, 350-361 (2005). Reviewer: Grigori N. Milstein (Ekaterinburg) MSC: 65C30 60H10 60H35 34F05 65L06 PDFBibTeX XMLCite \textit{F. Carbonell} et al., J. Comput. Appl. Math. 182, No. 2, 350--361 (2005; Zbl 1078.65004) Full Text: DOI
Rößler, Andreas Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise. (English) Zbl 1038.65003 J. Comput. Appl. Math. 164-165, 613-627 (2004). MSC: 65C30 65L06 60H35 60H10 34F05 65L20 PDFBibTeX XMLCite \textit{A. Rößler}, J. Comput. Appl. Math. 164--165, 613--627 (2004; Zbl 1038.65003) Full Text: DOI
Rössler, Andreas Coefficients of Runge-Kutta schemes for Itô stochastic differential equations. (English) Zbl 1354.65149 PAMM, Proc. Appl. Math. Mech. 3, 571-572 (2003). MSC: 65L06 60H10 PDFBibTeX XMLCite \textit{A. Rössler}, PAMM, Proc. Appl. Math. Mech. 3, 571--572 (2003; Zbl 1354.65149) Full Text: DOI
Lamba, H. An adaptive timestepping algorithm for stochastic differential equations. (English) Zbl 1037.65006 J. Comput. Appl. Math. 161, No. 2, 417-430 (2003). MSC: 65C30 34F05 65L50 65L70 60H10 60H35 65L05 PDFBibTeX XMLCite \textit{H. Lamba}, J. Comput. Appl. Math. 161, No. 2, 417--430 (2003; Zbl 1037.65006) Full Text: DOI
Burrage, Kevin; Tian, Tianhai Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. (English) Zbl 0991.65005 Comput. Phys. Commun. 142, No. 1-3, 186-190 (2001). MSC: 65C30 60H10 65L20 65L06 60H35 PDFBibTeX XMLCite \textit{K. Burrage} and \textit{T. Tian}, Comput. Phys. Commun. 142, No. 1--3, 186--190 (2001; Zbl 0991.65005) Full Text: DOI
Tian, Tianhai; Burrage, Kevin Implicit Taylor methods for stiff stochastic differential equations. (English) Zbl 0983.65007 Appl. Numer. Math. 38, No. 1-2, 167-185 (2001). Reviewer: Melvin D.Lax (Long Beach) MSC: 65C30 34F05 65L06 60H10 60H35 PDFBibTeX XMLCite \textit{T. Tian} and \textit{K. Burrage}, Appl. Numer. Math. 38, No. 1--2, 167--185 (2001; Zbl 0983.65007) Full Text: DOI
Burrage, Kevin; Tian, Tianhai The composite Euler method for stiff stochastic differential equations. (English) Zbl 0987.65009 J. Comput. Appl. Math. 131, No. 1-2, 407-426 (2001). Reviewer: Melvin D.Lax (Long Beach) MSC: 65C30 65L06 65L20 65H10 60H35 34F05 PDFBibTeX XMLCite \textit{K. Burrage} and \textit{T. Tian}, J. Comput. Appl. Math. 131, No. 1--2, 407--426 (2001; Zbl 0987.65009) Full Text: DOI
Burrage, Kevin; Burrage, Pamela; Mitsui, Taketomo Numerical solutions of stochastic differential equations – implementation and stability issues. (English) Zbl 0971.65003 J. Comput. Appl. Math. 125, No. 1-2, 171-182 (2000). Reviewer: Melvin D.Lax (Long Beach) MSC: 65C30 65L50 65L06 65L70 60H10 34F05 PDFBibTeX XMLCite \textit{K. Burrage} et al., J. Comput. Appl. Math. 125, No. 1--2, 171--182 (2000; Zbl 0971.65003) Full Text: DOI
Burrage, K.; Burrage, P. M. High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. (English) Zbl 1194.65023 Physica D 133, No. 1-4, 34-48 (1999). MSC: 65C30 60H10 60H35 PDFBibTeX XMLCite \textit{K. Burrage} and \textit{P. M. Burrage}, Physica D 133, No. 1--4, 34--48 (1999; Zbl 1194.65023) Full Text: DOI
Burrage, K.; Burrage, P. M.; Belward, J. A. A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations. (English) Zbl 0890.65146 BIT 37, No. 4, 771-780 (1997). Reviewer: M.D.Lax (Long Beach) MSC: 65C99 65L06 60H10 PDFBibTeX XMLCite \textit{K. Burrage} et al., BIT 37, No. 4, 771--780 (1997; Zbl 0890.65146) Full Text: DOI