A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

Year:    2016

Author:    Francisco Bernal, Juan A. Acebrón

Communications in Computational Physics, Vol. 20 (2016), Iss. 3 : pp. 703–732

Abstract

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the time step $h$ higher than $\mathcal{O}$$(√h)$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to R48. The paper is self-contained and the code will be made freely downloadable.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2015-0016

Communications in Computational Physics, Vol. 20 (2016), Iss. 3 : pp. 703–732

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:   

Author Details

Francisco Bernal

Juan A. Acebrón

  1. The Epidemiological and Economic Impact of COVID-19 in Kazakhstan: An Agent-Based Modeling

    Koichubekov, Berik | Takuadina, Aliya | Korshukov, Ilya | Sorokina, Marina | Turmukhambetova, Anar

    Healthcare, Vol. 11 (2023), Iss. 22 P.2968

    https://doi.org/10.3390/healthcare11222968 [Citations: 2]
  2. An Implementation of Milstein’s Method for General Bounded Diffusions

    Bernal, Francisco

    Journal of Scientific Computing, Vol. 79 (2019), Iss. 2 P.867

    https://doi.org/10.1007/s10915-018-0884-6 [Citations: 6]
  3. A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method

    Milewski, Sławomir

    Numerical Algorithms, Vol. 83 (2020), Iss. 2 P.565

    https://doi.org/10.1007/s11075-019-00694-x [Citations: 1]
  4. An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems

    Mancini, Sara | Bernal, Francisco | Acebrón, Juan A.

    Journal of Scientific Computing, Vol. 66 (2016), Iss. 2 P.577

    https://doi.org/10.1007/s10915-015-0033-4 [Citations: 7]
  5. Hybrid PDE solver for data-driven problems and modern branching

    BERNAL, FRANCISCO | DOS REIS, GONÇALO | SMITH, GREIG

    European Journal of Applied Mathematics, Vol. 28 (2017), Iss. 6 P.949

    https://doi.org/10.1017/S0956792517000109 [Citations: 5]
  6. A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs

    Bernal, Francisco | Morón-Vidal, Jorge | Acebrón, Juan A.

    Computers & Mathematics with Applications, Vol. 146 (2023), Iss. P.294

    https://doi.org/10.1016/j.camwa.2023.07.004 [Citations: 2]
  7. A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems

    Merle, Fabian | Prohl, Andreas

    Numerische Mathematik, Vol. 153 (2023), Iss. 4 P.827

    https://doi.org/10.1007/s00211-023-01350-2 [Citations: 2]
  8. On the Stochastic Modeling of COVID-19 under the Environmental White Noise

    Hussain, Shah | Madi, Elissa Nadia | Khan, Hasib | Gulzar, Haseena | Etemad, Sina | Rezapour, Shahram | Kaabar, Mohammed K. A. | Avery, Richard I.

    Journal of Function Spaces, Vol. 2022 (2022), Iss. P.1

    https://doi.org/10.1155/2022/4320865 [Citations: 24]
  9. Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan

    Koichubekov, Berik | Takuadina, Aliya | Korshukov, Ilya | Turmukhambetova, Anar | Sorokina, Marina

    Healthcare, Vol. 11 (2023), Iss. 5 P.752

    https://doi.org/10.3390/healthcare11050752 [Citations: 1]
  10. A multigrid-like algorithm for probabilistic domain decomposition

    Bernal, Francisco | Acebrón, Juan A.

    Computers & Mathematics with Applications, Vol. 72 (2016), Iss. 7 P.1790

    https://doi.org/10.1016/j.camwa.2016.07.030 [Citations: 5]