{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:30:55Z","timestamp":1773081055826,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,2,11]],"date-time":"2012-02-11T00:00:00Z","timestamp":1328918400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2012,11]]},"DOI":"10.1007\/s11075-012-9544-3","type":"journal-article","created":{"date-parts":[[2012,2,10]],"date-time":"2012-02-10T02:59:28Z","timestamp":1328842768000},"page":"479-498","source":"Crossref","is-referenced-by-count":3,"title":["A stepsize control algorithm for SDEs with small noise based on stochastic Runge\u2013Kutta Maruyama methods"],"prefix":"10.1007","volume":"61","author":[{"given":"A.","family":"Valinejad","sequence":"first","affiliation":[]},{"given":"S. Mohammad","family":"Hosseini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,2,11]]},"reference":[{"issue":"4","key":"9544_CR1","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/s10543-006-0098-4","volume":"46","author":"J Alcock","year":"2006","unstructured":"Alcock, J., Burrage, K.: A note on the Balanced method. BIT Numer. Math. 46(4), 689\u2013710 (2006)","journal-title":"BIT Numer. Math."},{"key":"9544_CR2","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.cam.2006.08.012","volume":"206","author":"AF Bastani","year":"2007","unstructured":"Bastani, A.F., Hosseini, S.M.: A new adaptive Runge-Kutta method for stochastic differential equations. J. Comput. Appl. Math. 206, 631\u2013644 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"9544_CR3","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.cam.2008.05.037","volume":"224","author":"AF Bastani","year":"2009","unstructured":"Bastani, A.F., Hosseini, S.M.: On mean-square stability properties of a new adaptive stochastic Runge-Kutta method. J. Comput. Appl. Math. 224, 556\u2013564 (2009)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"9544_CR4","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1137\/040602857","volume":"44","author":"E Buckwar","year":"2006","unstructured":"Buckwar, E., Winkler, R.: Multistep methods for SDEs and their applicationto problem with small noise. SIAM J. Numer. Anal. 44(2), 779\u2013803 (2006)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"9544_CR5","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1137\/090763275","volume":"32","author":"E Buckwar","year":"2010","unstructured":"Buckwar, E., R\u00f6\u00dfler, A., Winkler, R.: Stochastic Runge\u2013Kutta Methods for $It\\hat{o}$ SODEs with small noise. SIAM J. Sci. Comput. 32(4), 1789\u20131808 (2010)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"9544_CR6","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1016\/j.cam.2011.08.001","volume":"236","author":"E Buckwar","year":"2011","unstructured":"Buckwar, E., Riedler, M.G.: Runge\u2013Kutta methods for jump diffusion differential equation. J. Comput. Appl. Math. 236(6), 1155\u20131182 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"9544_CR7","unstructured":"Burrage. P.M.: Runge\u2013Kutta methods for stochastic differential equations. PhD thesis, University of Queensland, Australia (1999)"},{"issue":"3","key":"9544_CR8","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1137\/S1064827500376922","volume":"24","author":"PM Burrage","year":"2002","unstructured":"Burrage, P.M., Burrage, K.: A variable stepsize implementation for stochastic differential equations. SIAM J. Sci. Comput. 24(3), 848\u2013864 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"9544_CR9","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.cam.2004.01.027","volume":"170","author":"PM Burrage","year":"2004","unstructured":"Burrage, P.M., Herdiana, R., Burrage, K.: Adaptive stepsize based on control theory for stochastic differential equations. J. Comput. Appl. Math. 170(2), 317\u2013336 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"9544_CR10","doi-asserted-by":"crossref","DOI":"10.1002\/0470868279","volume-title":"Numerical Methods for Ordinary Differential Equations","author":"JC Butcher","year":"2003","unstructured":"Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, Chichester (2003)"},{"key":"9544_CR11","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1080\/13873950500064400","volume":"13","author":"G Denk","year":"2007","unstructured":"Denk, G., Winkler, R.: Modeling and simulation of transient noise in circuit simulation. Math. Comput. Model. Dyn. Syst. 13, 383\u2013394 (2007)","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"9544_CR12","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1016\/j.cub.2005.05.056","volume":"15","author":"AA Faisal","year":"2005","unstructured":"Faisal, A.A., White, J.A., Laughlin, S.B.: Ion channel noise places limits to the miniaturization of the brains wiring. Curr. Biol. 15, 1143\u20131149 (2005)","journal-title":"Curr. Biol."},{"issue":"5","key":"9544_CR13","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1137\/S0036139995286515","volume":"57","author":"JG Gaines","year":"1997","unstructured":"Gaines, J.G., Lyons, T.J.: Variable stepsize control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math. 57(5), 1455\u20131484 (1997)","journal-title":"SIAM J. Appl. Math."},{"key":"9544_CR14","volume-title":"Solving Ordinary Differential Equations I","author":"E Hairer","year":"1993","unstructured":"Hairer, E., N\u00f8rsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I. Springer, Berlin (1993)"},{"key":"9544_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-57913-4","volume-title":"Numerical Solution of SDE Through Computer Experiments","author":"PE Kloeden","year":"1994","unstructured":"Kloeden, P.E., Platen, E., Schurz, H.: Numerical Solution of SDE Through Computer Experiments. Springer, Berlin (1994)"},{"key":"9544_CR16","volume-title":"Numerical Solution of Stochastic Differential Equations","author":"PE Kloeden","year":"1999","unstructured":"Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1999)"},{"key":"9544_CR17","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s11075-007-9108-0","volume":"44","author":"D K\u00fcpper","year":"2007","unstructured":"K\u00fcpper, D., Lehn, J., R\u00f6\u00dfler, A.: A stepsize control algorithm for the weak approximation of stochastic differential equations. Numer. Algorithms 44, 335\u2013346 (2007)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"9544_CR18","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.cam.2003.05.001","volume":"161","author":"H Lamba","year":"2003","unstructured":"Lamba, H.: An adaptive timestepping algorithm for stochastic differential equations. J. Comput. Appl. Math. 161(2), 417\u2013430 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9544_CR19","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0377-0427(98)00139-3","volume":"100","author":"S Mauthner","year":"1998","unstructured":"Mauthner, S.: Stepsize control in the numerical solution of stochastic differential equations. J. Comput. Appl. Math. 100, 93\u2013109 (1998)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"9544_CR20","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1137\/S1064827594278575","volume":"28","author":"GN Milstein","year":"1997","unstructured":"Milstein, G.N., Tretyakov, M.V.: Mean-square numerical methods for stochastic differential equations with small noise. SIAM J. Sci. Comput. 28(2), 1067\u20131087 (1997)","journal-title":"SIAM J. Sci. Comput."},{"key":"9544_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-10063-9","volume-title":"Stochastic Numerics for Mathematical Physics","author":"GN Milstein","year":"2004","unstructured":"Milstein, G.N., Tretyakov, M.V.: Stochastic Numerics for Mathematical Physics. Springer, Berlin (2004)"},{"issue":"1","key":"9544_CR22","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/pamm.200410005","volume":"4","author":"A R\u00f6\u00dfler","year":"2004","unstructured":"R\u00f6\u00dfler, A.: An adaptive discretization algorithm for the weak approximation of stochastic differential equations. Proc. Appl. Math. Mech. 4(1), 19\u201322 (2004)","journal-title":"Proc. Appl. Math. Mech."},{"issue":"2","key":"9544_CR23","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1137\/030601429","volume":"28","author":"W R\u00f6misch","year":"2006","unstructured":"R\u00f6misch, W., Winkler, R.: Stepsize control for mean-squar numerical methods for stochastic differential equations with small noise. SIAM J. Sci. Comput. 28(2), 604\u2013625 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9544_CR24","volume-title":"Efficient Transient Noise Analysis in Circuit Simulation","author":"T Sickenberger","year":"2008","unstructured":"Sickenberger, T.: Efficient Transient Noise Analysis in Circuit Simulation. Logos-Verlag, Berlin (2008)"},{"key":"9544_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/641876.641877","volume":"29","author":"G S\u00f6derlind","year":"2003","unstructured":"S\u00f6derlind, G.: Digital filters in adaptive time-stepping. ACM Trans. Math. Software 29, 1\u201326 (2003)","journal-title":"ACM Trans. Math. Software"},{"key":"9544_CR26","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.apnum.2005.04.026","volume":"56","author":"G S\u00f6derlind","year":"2006","unstructured":"S\u00f6derlind, G.: Time-step algorithms: adaptivity, control and signal processing. Appl. Numer. Math. 56, 488\u2013502 (2006)","journal-title":"Appl. Numer. Math."},{"issue":"10","key":"9544_CR27","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1002\/cpa.10000","volume":"54","author":"A Szepessy","year":"2001","unstructured":"Szepessy, A., Tempone, R., Zouraris, G.: Adaptive weak approximation of stochastic differential equations. Commun. Pure Appl. Math. 54(10), 1169\u20131214 (2001)","journal-title":"Commun. Pure Appl. Math."},{"key":"9544_CR28","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/S0377-0427(03)00436-9","volume":"157","author":"R Winkler","year":"2003","unstructured":"Winkler, R.: Stochastic differential algebraic equations of index 1 and applications in circuit simulation. J. Comput. Appl. Math. 157, 477\u2013505 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9544_CR29","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/s11075-010-9363-3","volume":"55","author":"A Valinejad","year":"2010","unstructured":"Valinejad, A., Hosseini, S.M.: A variable step-size control algorithm for the weak approximation of Stochastic differential equations. J. Numer. Algor. 55, 429\u2013446 (2010)","journal-title":"J. Numer. Algor."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9544-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-012-9544-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9544-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:17Z","timestamp":1559365697000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-012-9544-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,11]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,11]]}},"alternative-id":["9544"],"URL":"https:\/\/doi.org\/10.1007\/s11075-012-9544-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,11]]}}}