179
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Shooting Methods for Numerical Solution of Nonlinear Stochastic Boundary-Value Problems

Pages 187-200 | Received 13 Jul 2006, Accepted 08 Sep 2006, Published online: 15 Dec 2006

REFERENCES

  • Allen , E.J. , and Nunn , C.J. 1995 . Difference methods for numerical solution of stochastic two-point boundary-value problems . In: Proceedings of the First International Conference on Difference Equations . Elydi , S. N. , Greef , J. R. , Ladas , G. , Peterson , A. C. (eds)., Gordan and Breach Publishers , Amsterdam .
  • Arciniega , A. , and Allen , E. 2003 . Rounding error in numerical solution of stochastic differential equations . Stoch. Anal. Appl. 21 ( 2 ): 281 – 300 . [CSA]
  • Arciniega , A. , and Allen , E. 2004 . Shooting methods for numerical solution of stochastic boundary-value problems . Stoch. Anal. Appl. 22 ( 5 ): 1295 – 1314 . [CSA] [CROSSREF]
  • Arnold , L. 1974 . Stochastic Differential Equations: Theory and Applications . John Wiley & Sons , New York .
  • Gard , T.C. 1988 . Introduction to Stochastic Differential Equations . Marcel Dekker , New York .
  • Keller , H.B. 1968. Numerical Methods for Two-Point Boundary-Value Problems . Blaisdell Publishing Co. , Massachusetts.
  • Kloeden , P.E. , and Platen , E. 1992 . Numerical Solution of Stochastic Differential Equations . Springer-Verlag , New York .
  • Kloeden , P.E. , Platen , E. , and Schurz , H. 1994 . Numerical Solution of SDE Through Computer Experiments . Springer-Verlag , Berlin .
  • Milstein , G.N. , and Tretyakov , M.V. 2004 . Stochastic Numerics for Mathematical Physics . Springer-Verlag , Berlin .
  • Nualart , D. , and Pardoux , E. 1991 . Boundary value problems for stochastic differential equations . The Annals of Probability 19 ( 4 ): 1118 – 1144 . [CSA]
  • Nualart , D. , and Pardoux , E. 1991 . Second order stochastic differential equations with Dirichlet boundary conditions . Stochastic Process Appl. 39 ( 1 ): 1 – 24 . [CSA] [CROSSREF]
  • Ocone , D. , and Pardoux , E. 1989 . Linear stochastic differential equations with boundary conditions . Probability Theory and Related Fields 82 : 489 – 526 . [CSA] [CROSSREF]
  • Ortega , J.M. 1972 . Numerical Analysis: A Second Course . Academic Press, Inc. , London .
  • Sharp , W.D. , and Allen , E.J. 2000 . Stochastic neutron transport equations for rod and plane geometries . Annals of Nuclear Energy 27 ( 2 ): 99 – 116 . [CSA] [CROSSREF]
  • Talay , D. 1995 . Simulation and numerical analysis of stochastic differential systems: a review . In: Probabilistic Methods in Applied Physics . Kree , P. , Wedig , W. , (eds). Lecture Notes in Physics , Springer-Verlag , New York , 451 , 63 – 106 .
  • Talay , D. , and Turbano , L. 1990 . Expansion of the global error for numerical schemes solving stochastic differential equations . Stoch. Anal. Appl. 8 ( 4 ): 483 – 509 . [CSA]
  • Zeitouni , O. , and Dembo , A. 1990 . A change of variables formula for stratonovich integrals and existence of solutions for two-point stochastic boundary value problems . Probability Theory and Related Fields 84 : 411 – 425 . [CSA] [CROSSREF]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.