메뉴 건너뛰기




Volumn 52, Issue 2, 2012, Pages 437-455

A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise

Author keywords

Mean square convergence; Mean square stability; Stiffly accurate; Stochastic differential algebraic equation; Stochastic Runge Kutta method

Indexed keywords


EID: 84862580470     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-011-0354-0     Document Type: Article
Times cited : (15)

References (19)
  • 1
    • 0001266425 scopus 로고
    • Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s
    • Alexander, R.: Diagonally implicit Runge-Kutta methods for stiff O. D. E.'s. SIAM J. Numer. Anal. 14(6), 1006-1021 (1977).
    • (1977) SIAM J. Numer. Anal. , vol.14 , Issue.6 , pp. 1006-1021
    • Alexander, R.1
  • 2
    • 0004003433 scopus 로고    scopus 로고
    • Classics in Applied MathematicsRevised and corrected reprint of the 1989 original, Philadelphia: Society for Industrial and Applied Mathematics (SIAM)
    • Brenan, K. E., Campbell, S. L., Petzold, L. R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Classics in Applied Mathematics, vol. 14. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1996). Revised and corrected reprint of the 1989 original.
    • (1996) Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations , vol.14
    • Brenan, K.E.1    Campbell, S.L.2    Petzold, L.R.3
  • 3
    • 4043136017 scopus 로고    scopus 로고
    • Implicit stochastic Runge-Kutta methods for stochastic differential equations
    • doi:10.1023/B:BITN.0000025089.50729.0f
    • Burrage, K., Tian, T.: Implicit stochastic Runge-Kutta methods for stochastic differential equations. BIT Numer. Math. 44(1), 21-39 (2004). doi: 10. 1023/B: BITN. 0000025089. 50729. 0f.
    • (2004) BIT Numer. Math. , vol.44 , Issue.1 , pp. 21-39
    • Burrage, K.1    Tian, T.2
  • 4
    • 58249088540 scopus 로고    scopus 로고
    • B-series analysis of stochastic Runge-Kutta methods that use an iterative scheme to compute their internal stage values
    • doi:10.1137/070704307
    • Debrabant, K., Kværnø, A.: B-series analysis of stochastic Runge-Kutta methods that use an iterative scheme to compute their internal stage values. SIAM J. Numer. Anal. 47(1), 181-203 (2008/09). doi: 10. 1137/070704307.
    • (2008) SIAM J. Numer. Anal. , vol.47 , Issue.1 , pp. 181-203
    • Debrabant, K.1    Kværnø, A.2
  • 5
    • 58249086593 scopus 로고    scopus 로고
    • Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
    • doi:10.1016/j.apnum.2008.03.011
    • Debrabant, K., Rößler, A.: Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis. Appl. Numer. Math. 59(3-4), 595-607 (2009). doi: 10. 1016/j. apnum. 2008. 03. 011.
    • (2009) Appl. Numer. Math. , vol.59 , Issue.3-4 , pp. 595-607
    • Debrabant, K.1    Rößler, A.2
  • 7
    • 0003589989 scopus 로고    scopus 로고
    • 2nd edn., Springer Series in Computational MathematicsStiff and differential-algebraic problems, Berlin: Springer
    • Hairer, E., Wanner, G.: Solving Ordinary Differential Equations. II, 2nd edn. Springer Series in Computational Mathematics, vol. 14. Springer, Berlin (2002). Stiff and differential-algebraic problems.
    • (2002) Solving Ordinary Differential Equations. II , vol.14
    • Hairer, E.1    Wanner, G.2
  • 8
    • 0034436594 scopus 로고    scopus 로고
    • Mean-square and asymptotic stability of the stochastic theta method
    • electronic, doi:10.1137/S003614299834736X
    • Higham, D. J.: Mean-square and asymptotic stability of the stochastic theta method. SIAM J. Numer. Anal. 38(3), 753-769 (electronic) (2000). doi: 10. 1137/S003614299834736X.
    • (2000) SIAM J. Numer. Anal. , vol.38 , Issue.3 , pp. 753-769
    • Higham, D.J.1
  • 12
    • 33947271619 scopus 로고    scopus 로고
    • Stochastic DAEs in circuit simulation
    • Oberwolfach2001Internat. Ser. Numer. Math, Basel: Birkhäuser
    • Römisch, W., Winkler, R.: Stochastic DAEs in circuit simulation. In: Modeling, Simulation, and Optimization of Integrated Circuits (Oberwolfach, 2001). Internat. Ser. Numer. Math., vol. 146, pp. 303-318. Birkhäuser, Basel (2003).
    • (2003) Modeling, Simulation, and Optimization of Integrated Circuits , vol.146 , pp. 303-318
    • Römisch, W.1    Winkler, R.2
  • 13
    • 77956044362 scopus 로고    scopus 로고
    • Runge-Kutta methods for the strong approximation of solutions of stochastic differential equations
    • doi:10.1137/09076636X
    • Rößler, A.: Runge-Kutta methods for the strong approximation of solutions of stochastic differential equations. SIAM J. Numer. Anal. 48(3), 922-952 (2010). doi: 10. 1137/09076636X.
    • (2010) SIAM J. Numer. Anal. , vol.48 , Issue.3 , pp. 922-952
    • Rößler, A.1
  • 14
    • 77951187649 scopus 로고    scopus 로고
    • Stochastic Taylor expansions for functionals of diffusion processes
    • doi:10.1080/07362991003707905
    • Rößler, A.: Stochastic Taylor expansions for functionals of diffusion processes. Stoch. Anal. Appl. 28(3), 415-429 (2010). doi: 10. 1080/07362991003707905.
    • (2010) Stoch. Anal. Appl. , vol.28 , Issue.3 , pp. 415-429
    • Rößler, A.1
  • 15
    • 0000007761 scopus 로고    scopus 로고
    • Stability analysis of numerical schemes for stochastic differential equations
    • doi:10.1137/S0036142992228409
    • Saito, Y., Mitsui, T.: Stability analysis of numerical schemes for stochastic differential equations. SIAM J. Numer. Anal. 33(6), 2254-2267 (1996). doi: 10. 1137/S0036142992228409.
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.6 , pp. 2254-2267
    • Saito, Y.1    Mitsui, T.2
  • 17
    • 0032205709 scopus 로고    scopus 로고
    • Numerical solution of stochastic differential-algebraic equations with applications to transient noise simulation of microelectronic circuits
    • doi:10.1016/S0377-0427(98)00138-1
    • Schein, O., Denk, G.: Numerical solution of stochastic differential-algebraic equations with applications to transient noise simulation of microelectronic circuits. J. Comput. Appl. Math. 100(1), 77-92 (1998). doi: 10. 1016/S0377-0427(98)00138-1.
    • (1998) J. Comput. Appl. Math. , vol.100 , Issue.1 , pp. 77-92
    • Schein, O.1    Denk, G.2
  • 18
    • 61849151876 scopus 로고    scopus 로고
    • Local error estimates for moderately smooth problems. II. SDEs and SDAEs with small noise
    • doi:10.1007/s10543-009-0209-0
    • Sickenberger, T., Weinmüller, E., Winkler, R.: Local error estimates for moderately smooth problems. II. SDEs and SDAEs with small noise. BIT Numer. Math. 49(1), 217-245 (2009). doi: 10. 1007/s10543-009-0209-0.
    • (2009) BIT Numer. Math , vol.49 , Issue.1 , pp. 217-245
    • Sickenberger, T.1    Weinmüller, E.2    Winkler, R.3
  • 19
    • 0041519194 scopus 로고    scopus 로고
    • Stochastic differential algebraic equations of index 1 and applications in circuit simulation
    • doi:10.1016/S0377-0427(03)00436-9
    • Winkler, R.: Stochastic differential algebraic equations of index 1 and applications in circuit simulation. J. Comput. Appl. Math. 157(2), 477-505 (2003). doi: 10. 1016/S0377-0427(03)00436-9.
    • (2003) J. Comput. Appl. Math. , vol.157 , Issue.2 , pp. 477-505
    • Winkler, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.