Deng, Chang-Song; Liu, Wei Semi-implicit Euler-Maruyama method for non-linear time-changed stochastic differential equations. (English) Zbl 1469.65028 BIT 60, No. 4, 1133-1151 (2020). MSC: 65C30 60H10 60J60 PDF BibTeX XML Cite \textit{C.-S. Deng} and \textit{W. Liu}, BIT 60, No. 4, 1133--1151 (2020; Zbl 1469.65028) Full Text: DOI arXiv OpenURL
Winters, Andrew R.; Czernik, Christof; Schily, Moritz B.; Gassner, Gregor J. Entropy stable numerical approximations for the isothermal and polytropic Euler equations. (English) Zbl 1446.65134 BIT 60, No. 3, 791-824 (2020). MSC: 65M70 65M12 35L35 35L60 35Q31 PDF BibTeX XML Cite \textit{A. R. Winters} et al., BIT 60, No. 3, 791--824 (2020; Zbl 1446.65134) Full Text: DOI arXiv OpenURL
Li, Libo; Taguchi, Dai On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case. (English) Zbl 1480.65017 BIT 59, No. 3, 747-774 (2019). MSC: 65C30 60H10 60H35 PDF BibTeX XML Cite \textit{L. Li} and \textit{D. Taguchi}, BIT 59, No. 3, 747--774 (2019; Zbl 1480.65017) Full Text: DOI arXiv OpenURL
Blömker, Dirk; Kamrani, Minoo Numerically computable a posteriori-bounds for the stochastic Allen-Cahn Equation. (English) Zbl 1433.60073 BIT 59, No. 3, 647-673 (2019). MSC: 60H35 65C30 60H15 35R60 PDF BibTeX XML Cite \textit{D. Blömker} and \textit{M. Kamrani}, BIT 59, No. 3, 647--673 (2019; Zbl 1433.60073) Full Text: DOI arXiv OpenURL
Guo, Ping; Li, Chong-Jun Razumikhin-type technique on stability of exact and numerical solutions for the nonlinear stochastic pantograph differential equations. (English) Zbl 1418.60057 BIT 59, No. 1, 77-96 (2019). MSC: 60H10 65L20 65C30 PDF BibTeX XML Cite \textit{P. Guo} and \textit{C.-J. Li}, BIT 59, No. 1, 77--96 (2019; Zbl 1418.60057) Full Text: DOI OpenURL
Kumar, Rakesh Adaptive semi-discrete formulation of BSQI-WENO scheme for the modified Burgers’ equation. (English) Zbl 1448.65108 BIT 58, No. 1, 103-132 (2018). MSC: 65M06 65M22 65M15 65L06 65D07 35Q53 35Q31 PDF BibTeX XML Cite \textit{R. Kumar}, BIT 58, No. 1, 103--132 (2018; Zbl 1448.65108) Full Text: DOI OpenURL
Lang, Annika; Petersson, Andreas; Thalhammer, Andreas Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions. (English) Zbl 1418.65005 BIT 57, No. 4, 963-990 (2017). MSC: 65C30 60H15 65M75 60H35 PDF BibTeX XML Cite \textit{A. Lang} et al., BIT 57, No. 4, 963--990 (2017; Zbl 1418.65005) Full Text: DOI arXiv OpenURL
Nipp, Kaspar; Stoffer, Daniel Invariant curves for the discretised van der Pol equation. (English) Zbl 1377.37043 BIT 57, No. 2, 463-497 (2017). Reviewer: Eszter Gselmann (Debrecen) MSC: 37D10 39A30 65L05 34E15 PDF BibTeX XML Cite \textit{K. Nipp} and \textit{D. Stoffer}, BIT 57, No. 2, 463--497 (2017; Zbl 1377.37043) Full Text: DOI OpenURL
Andersson, Adam; Kruse, Raphael Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition. (English) Zbl 1365.65010 BIT 57, No. 1, 21-53 (2017). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 65L06 65L20 60H10 60H35 34F05 65L12 65L04 PDF BibTeX XML Cite \textit{A. Andersson} and \textit{R. Kruse}, BIT 57, No. 1, 21--53 (2017; Zbl 1365.65010) Full Text: DOI arXiv OpenURL
Svärd, Magnus Entropy solutions of the compressible Euler equations. (English) Zbl 1362.35223 BIT 56, No. 4, 1479-1496 (2016). Reviewer: Bernard Ducomet (Bruyères le Châtel) MSC: 35Q31 35L65 65M12 76N10 35D30 65M06 PDF BibTeX XML Cite \textit{M. Svärd}, BIT 56, No. 4, 1479--1496 (2016; Zbl 1362.35223) Full Text: DOI Link OpenURL
Shardlow, Tony; Taylor, Phillip On the pathwise approximation of stochastic differential equations. (English) Zbl 1354.65016 BIT 56, No. 3, 1101-1129 (2016). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 60H10 60H35 34F05 65L70 PDF BibTeX XML Cite \textit{T. Shardlow} and \textit{P. Taylor}, BIT 56, No. 3, 1101--1129 (2016; Zbl 1354.65016) Full Text: DOI arXiv Link OpenURL
Leobacher, Gunther; Szölgyenyi, Michaela A numerical method for SDEs with discontinuous drift. (English) Zbl 1341.65005 BIT 56, No. 1, 151-162 (2016). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 60H10 60H35 34F05 65L20 PDF BibTeX XML Cite \textit{G. Leobacher} and \textit{M. Szölgyenyi}, BIT 56, No. 1, 151--162 (2016; Zbl 1341.65005) Full Text: DOI arXiv OpenURL
Das, Pratibhamoy; Mehrmann, Volker Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters. (English) Zbl 1341.65031 BIT 56, No. 1, 51-76 (2016). Reviewer: Srinivasan Natesan (Assam) MSC: 65M06 65M12 65M50 35K20 35B25 PDF BibTeX XML Cite \textit{P. Das} and \textit{V. Mehrmann}, BIT 56, No. 1, 51--76 (2016; Zbl 1341.65031) Full Text: DOI Link OpenURL
Beck, Mélanie; Gander, Martin J. On the positivity of Poisson integrators for the Lotka-Volterra equations. (English) Zbl 1321.65184 BIT 55, No. 2, 319-340 (2015). Reviewer: Drahoslava Janovská (Praha) MSC: 65P10 37M15 65L20 65L70 PDF BibTeX XML Cite \textit{M. Beck} and \textit{M. J. Gander}, BIT 55, No. 2, 319--340 (2015; Zbl 1321.65184) Full Text: DOI OpenURL
Komori, Yoshio; Burrage, Kevin A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. (English) Zbl 1307.65011 BIT 54, No. 4, 1067-1085 (2014). MSC: 65C30 60H10 60H35 34F05 92E20 PDF BibTeX XML Cite \textit{Y. Komori} and \textit{K. Burrage}, BIT 54, No. 4, 1067--1085 (2014; Zbl 1307.65011) Full Text: DOI OpenURL
Hansen, Eskil; Stillfjord, Tony Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay. (English) Zbl 1304.65188 BIT 54, No. 3, 673-689 (2014). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65M06 65M15 35K55 35R10 65M12 PDF BibTeX XML Cite \textit{E. Hansen} and \textit{T. Stillfjord}, BIT 54, No. 3, 673--689 (2014; Zbl 1304.65188) Full Text: DOI Link OpenURL
Barth, Andrea; Lang, Annika; Schwab, Christoph Multilevel Monte Carlo method for parabolic stochastic partial differential equations. (English) Zbl 1272.65009 BIT 53, No. 1, 3-27 (2013). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 60H15 60H35 65C05 35R60 35K20 65M12 65Y20 PDF BibTeX XML Cite \textit{A. Barth} et al., BIT 53, No. 1, 3--27 (2013; Zbl 1272.65009) Full Text: DOI Link OpenURL
Szpruch, Lukasz; Mao, Xuerong; Higham, Desmond J.; Pan, Jiazhu Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. (English) Zbl 1230.65011 BIT 51, No. 2, 405-425 (2011). Reviewer: Gong Guanglu (Beijing) MSC: 65C30 60H10 60H35 34F05 65C05 91G30 91G60 PDF BibTeX XML Cite \textit{L. Szpruch} et al., BIT 51, No. 2, 405--425 (2011; Zbl 1230.65011) Full Text: DOI OpenURL
Higham, Desmond J.; Intep, Somkid; Mao, Xuerong; Szpruch, Lukasz Hybrid simulation of autoregulation within transcription and translation. (English) Zbl 1211.92020 BIT 51, No. 1, 177-196 (2011). MSC: 92C40 92-08 60H10 65C20 92D10 92C45 PDF BibTeX XML Cite \textit{D. J. Higham} et al., BIT 51, No. 1, 177--196 (2011; Zbl 1211.92020) Full Text: DOI OpenURL
Butcher, J. C.; Chan, T. M. H. The tree and forest spaces with applications to initial-value problem methods. (English) Zbl 1205.65211 BIT 50, No. 4, 713-728 (2010). MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{J. C. Butcher} and \textit{T. M. H. Chan}, BIT 50, No. 4, 713--728 (2010; Zbl 1205.65211) Full Text: DOI OpenURL
Halidias, Nikolaos; Kloeden, Peter E. A note on the Euler-Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient. (English) Zbl 1136.65008 BIT 48, No. 1, 51-59 (2008). MSC: 65C30 60H10 60H35 34F05 PDF BibTeX XML Cite \textit{N. Halidias} and \textit{P. E. Kloeden}, BIT 48, No. 1, 51--59 (2008; Zbl 1136.65008) Full Text: DOI OpenURL
Rößler, Andreas Second order Runge-Kutta methods for Stratonovich stochastic differential equations. (English) Zbl 1127.65007 BIT 47, No. 3, 657-680 (2007). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 65L06 60H35 60H10 PDF BibTeX XML Cite \textit{A. Rößler}, BIT 47, No. 3, 657--680 (2007; Zbl 1127.65007) Full Text: DOI OpenURL
Müller-Gronbach, Thomas; Ritter, Klaus An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise. (English) Zbl 1127.65006 BIT 47, No. 2, 393-418 (2007). Reviewer: Eckhard Platen (Broadway) MSC: 65C30 60H15 60H35 65M06 65M15 PDF BibTeX XML Cite \textit{T. Müller-Gronbach} and \textit{K. Ritter}, BIT 47, No. 2, 393--418 (2007; Zbl 1127.65006) Full Text: DOI arXiv OpenURL
Ascher, U. M.; Huang, H.; van den Doel, K. Artificial time integration. (English) Zbl 1113.65068 BIT 47, No. 1, 3-25 (2007). MSC: 65L05 34A34 34A26 65K10 49Q10 65M32 65D18 65N21 PDF BibTeX XML Cite \textit{U. M. Ascher} et al., BIT 47, No. 1, 3--25 (2007; Zbl 1113.65068) Full Text: DOI Link OpenURL
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 OpenURL
Higham, D. J.; Mao, X. Nonnormality and stochastic differential equations. (English) Zbl 1105.65007 BIT 46, No. 3, 525-532 (2006). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 34F05 60H10 65L20 65L06 65L07 PDF BibTeX XML Cite \textit{D. J. Higham} and \textit{X. Mao}, BIT 46, No. 3, 525--532 (2006; Zbl 1105.65007) Full Text: DOI OpenURL
Shardlow, Tony Modified equations for stochastic differential equations. (English) Zbl 1091.65005 BIT 46, No. 1, 111-125 (2006). MSC: 65C30 60H10 60H35 65L70 PDF BibTeX XML Cite \textit{T. Shardlow}, BIT 46, No. 1, 111--125 (2006; Zbl 1091.65005) Full Text: DOI OpenURL
Grimm, V.; Quispel, G. R. W. Geometric integration methods that preserve Lyapunov functions. (English) Zbl 1094.65070 BIT 45, No. 4, 709-723 (2005). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L06 65P40 65L05 37M25 34A34 34A26 65L20 PDF BibTeX XML Cite \textit{V. Grimm} and \textit{G. R. W. Quispel}, BIT 45, No. 4, 709--723 (2005; Zbl 1094.65070) Full Text: DOI OpenURL
Rathish Kumar, B. V.; Mehra, M. Wavelet-Taylor Galerkin method for the Burgers equation. (English) Zbl 1082.65101 BIT 45, No. 3, 543-560 (2005). MSC: 65M60 35Q53 65M15 65M12 PDF BibTeX XML Cite \textit{B. V. Rathish Kumar} and \textit{M. Mehra}, BIT 45, No. 3, 543--560 (2005; Zbl 1082.65101) Full Text: DOI Link OpenURL
Jakobsen, E. R.; Karlsen, K. H. Convergence rates for semi-discrete splitting approximations for degenerate parabolic equations with source teams. (English) Zbl 1079.65094 BIT 45, No. 1, 37-67 (2005). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M12 65M06 35L60 65M20 35K65 49J25 PDF BibTeX XML Cite \textit{E. R. Jakobsen} and \textit{K. H. Karlsen}, BIT 45, No. 1, 37--67 (2005; Zbl 1079.65094) Full Text: DOI OpenURL
Vermiglio, R.; Torelli, L. A stable numerical approach for implicit non-linear neutral delay differential equations. (English) Zbl 1030.65078 BIT 43, No. 1, 195-215 (2003). Reviewer: Neville Ford (Chester) MSC: 65L05 65L06 34K20 65L80 65L20 34K28 34K40 34A09 PDF BibTeX XML Cite \textit{R. Vermiglio} and \textit{L. Torelli}, BIT 43, No. 1, 195--215 (2003; Zbl 1030.65078) Full Text: DOI OpenURL
Bryden, Alan; Higham, Desmond J. On the boundedness of asymptotic stability regions for the stochastic theta method. (English) Zbl 1026.65004 BIT 43, No. 1, 1-6 (2003). Reviewer: Kevin Burrage (Brisbane) MSC: 65C30 60H10 60H35 65L20 PDF BibTeX XML Cite \textit{A. Bryden} and \textit{D. J. Higham}, BIT 43, No. 1, 1--6 (2003; Zbl 1026.65004) Full Text: DOI OpenURL
Lötstedt, Per; Söderberg, Stefan; Ramage, Alison; Hemmingsson-Frändén, Lina Implicit solution of hyerbolic equations with space-time adaptivity. (English) Zbl 0999.65084 BIT 42, No. 1, 134-158 (2002). Reviewer: P.B.Dubovski (Moskva) MSC: 65M06 65M50 35L65 65M12 65Y05 PDF BibTeX XML Cite \textit{P. Lötstedt} et al., BIT 42, No. 1, 134--158 (2002; Zbl 0999.65084) Full Text: DOI OpenURL
Grüne, L.; Kloeden, P. E. Pathwise approximation of random ordinary differential equations. (English) Zbl 0998.65010 BIT 41, No. 4, 711-721 (2001). Reviewer: Melvin D.Lax (Long Beach) MSC: 65C30 65L06 34F05 65L20 60H10 60H35 65L70 PDF BibTeX XML Cite \textit{L. Grüne} and \textit{P. E. Kloeden}, BIT 41, No. 4, 711--721 (2001; Zbl 0998.65010) Full Text: DOI OpenURL
Burrage, K.; Piskarev, S. Stochastic methods for ill-posed problems. (English) Zbl 0960.65011 BIT 40, No. 2, 226-240 (2000). Reviewer: Eckhard Platen (Broadway) MSC: 65C30 60H10 65L08 34A34 65L06 65L20 PDF BibTeX XML Cite \textit{K. Burrage} and \textit{S. Piskarev}, BIT 40, No. 2, 226--240 (2000; Zbl 0960.65011) Full Text: DOI OpenURL
Owren, B.; Welfert, B. The Newton iteration on Lie groups. (English) Zbl 0957.65054 BIT 40, No. 1, 121-145 (2000). Reviewer: Etienne Emmrich (Berlin) MSC: 65J15 22E30 34C40 65L05 47J25 PDF BibTeX XML Cite \textit{B. Owren} and \textit{B. Welfert}, BIT 40, No. 1, 121--145 (2000; Zbl 0957.65054) Full Text: DOI OpenURL
Koto, T. Naimark-Sacker bifurcations in the Euler method for a delay differential equation. (English) Zbl 0918.65054 BIT 39, No. 1, 110-115 (1999). Reviewer: P.Chocholatý (Bratislava) MSC: 65L05 65L20 34K05 34C23 PDF BibTeX XML Cite \textit{T. Koto}, BIT 39, No. 1, 110--115 (1999; Zbl 0918.65054) Full Text: DOI OpenURL
Auzinger, W.; Frank, R.; Kirlinger, G. Extending convergence theory for nonlinear stiff problems. I. (English) Zbl 0863.65040 BIT 36, No. 4, 635-652 (1996). Reviewer: E.Hairer (Genève) MSC: 65L05 34E13 65L70 34A34 PDF BibTeX XML Cite \textit{W. Auzinger} et al., BIT 36, No. 4, 635--652 (1996; Zbl 0863.65040) Full Text: DOI OpenURL
Arévalo, C.; Führer, C.; Söderlind, G. Stabilized multistep methods for index 2 Euler-Lagrange DAEs. (English) Zbl 0854.65065 BIT 36, No. 1, 1-13 (1996). Reviewer: R.Lamour (Berlin) MSC: 65L06 65L05 65L20 70F10 34A34 34A09 PDF BibTeX XML Cite \textit{C. Arévalo} et al., BIT 36, No. 1, 1--13 (1996; Zbl 0854.65065) Full Text: DOI OpenURL
Arévalo, Carmen; Lötstedt, Per Improving the accuracy of BDF methods for index 3 differential-algebraic equations. (English) Zbl 0845.65030 BIT 35, No. 3, 297-308 (1995). Reviewer: M.Gousidou-Koutita (Thessaloniki) MSC: 65L05 65L70 34A34 34A09 65L50 PDF BibTeX XML Cite \textit{C. Arévalo} and \textit{P. Lötstedt}, BIT 35, No. 3, 297--308 (1995; Zbl 0845.65030) Full Text: DOI OpenURL
Bjørhus, Morten A note on the convergence of discretized dynamic iteration. (English) Zbl 0833.65074 BIT 35, No. 2, 291-296 (1995). Reviewer: F.Zhang (Singapore) MSC: 65L06 65L05 65L70 34A34 PDF BibTeX XML Cite \textit{M. Bjørhus}, BIT 35, No. 2, 291--296 (1995; Zbl 0833.65074) Full Text: DOI OpenURL
Sand, Jørgen; Skelboe, Stig Stability of backward Euler multirate methods and convergence of waveform relaxation. (English) Zbl 0760.65086 BIT 32, No. 2, 350-366 (1992). Reviewer: J.H.Verner (Kingston / Ontario) MSC: 65L20 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{J. Sand} and \textit{S. Skelboe}, BIT 32, No. 2, 350--366 (1992; Zbl 0760.65086) Full Text: DOI OpenURL
Skelboe, Stig Methods for parallel integration of stiff systems of ODEs. (English) Zbl 0765.65075 BIT 32, No. 4, 689-701 (1992). Reviewer: W.Schönauer (Karlsruhe) MSC: 65L05 65L20 65Y05 34A34 34E13 PDF BibTeX XML Cite \textit{S. Skelboe}, BIT 32, No. 4, 689--701 (1992; Zbl 0765.65075) Full Text: DOI OpenURL
Hansbo, Anita Error estimates for the numerical solution of a time-periodic linear parabolic problem. (English) Zbl 0780.65057 BIT 31, No. 4, 664-685 (1991). Reviewer: U.Langer (Chemnitz) MSC: 65M15 65M20 65M60 35K15 PDF BibTeX XML Cite \textit{A. Hansbo}, BIT 31, No. 4, 664--685 (1991; Zbl 0780.65057) Full Text: DOI OpenURL
Lubich, Ch. On projected Runge-Kutta methods for differential-algebraic equations. (English) Zbl 0764.65041 BIT 31, No. 3, 545-550 (1991). Reviewer: H.Weber (Wiesbaden) MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{Ch. Lubich}, BIT 31, No. 3, 545--550 (1991; Zbl 0764.65041) Full Text: DOI OpenURL
Kreiss, Gunilla Convergence to steady state of solutions of the Euler equations. I. (English) Zbl 0651.76027 BIT 28, No. 1, 144-162 (1988). MSC: 76N10 65N99 76M99 35Q30 PDF BibTeX XML Cite \textit{G. Kreiss}, BIT 28, No. 1, 144--162 (1988; Zbl 0651.76027) Full Text: DOI OpenURL
Söderlind, Gustaf On nonlinear difference and differential equations. (English) Zbl 0557.65043 BIT 24, 667-680 (1984). Reviewer: G.J.Cooper MSC: 65L05 65Q05 39A10 34A34 PDF BibTeX XML Cite \textit{G. Söderlind}, BIT 24, 667--680 (1984; Zbl 0557.65043) Full Text: DOI OpenURL
Kacewicz, Boleslaw Optimality of Euler-integral information for solving a scalar autonomous ODE. (English) Zbl 0516.65055 BIT 23, 217-230 (1983). MSC: 65L05 68Q25 PDF BibTeX XML Cite \textit{B. Kacewicz}, BIT 23, 217--230 (1983; Zbl 0516.65055) Full Text: DOI OpenURL