Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Comment on "Numerical methods for stochastic differential equations".

Kevin Burrage1, Pamela Burrage, Desmond J Higham

  • 1Advanced Computational Modelling Centre, University of Queensland, Brisbane QLD 4072, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A mathematical perspective on hypothesis-driven model construction: A case study in pea.

Mathematical biosciences·2026
Same author

Optimal control of multiple myeloma assuming drug resistance and off-target effects.

PLoS computational biology·2025
Same author

An in-depth study of the dynamics of Thornley's mathematical model in plant biology with a view to an improved model.

Journal of theoretical biology·2025
Same author

Agent-based modeling for the tumor microenvironment (TME).

Mathematical biosciences and engineering : MBE·2024
Same author

Harnessing 12-lead ECG and MRI data to personalise repolarisation profiles in cardiac digital twin models for enhanced virtual drug testing.

Medical image analysis·2024
Same author

How adversarial attacks can disrupt seemingly stable accurate classifiers.

Neural networks : the official journal of the International Neural Network Society·2024
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Deterministic calculus methods are invalid for stochastic differential equations, failing to achieve high-order accuracy. Readers should avoid applying these deterministic approaches in stochastic settings.

Area of Science:

  • Numerical analysis
  • Stochastic processes

Background:

  • Runge-Kutta methods are commonly used for ordinary differential equations.
  • A heuristic approach was previously applied to adapt these methods for stochastic differential equations.

Discussion:

  • The heuristic adaptation of deterministic Runge-Kutta methods for stochastic differential equations is generally invalid.
  • This approach does not yield the intended high-order accuracy for stochastic solutions.

Key Insights:

  • Deterministic calculus is inappropriate for stochastic settings.
  • The previously proposed methods lack general validity and do not achieve high order.

Outlook:

  • Further research is needed to develop accurate high-order numerical methods for stochastic differential equations.

Related Experiment Videos

  • Caution is advised when applying existing deterministic numerical techniques to stochastic problems.