Volume 13, Issue 1
Strong Backward Error Analysis for Euler-Maruyama Method

J. Deng

DOI:

Int. J. Numer. Anal. Mod., 13 (2016), pp. 1-21

Published online: 2016-01

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  • Abstract

Backward error analysis is an important tool to study long time behavior of numerical methods. The main idea of it is to use perturbed equations, namely modified equations, to represent the numerical solutions. Since stochastic backward error analysis has not been well developed so far. This paper investigates the stochastic modified equation and backward error analysis for Euler-Maruyama method with respect to strong convergence are built up. Like deterministic case, stochastic modified equations, expressed as formal series, do not converge in general. But there exists the optimal truncation of the series such that the one step error of the modified equations is sub-exponentially small with respect to time step. Moreover, the result of stochastic backward error analysis is used to study the error growth of the Euler-Maruyama method on Kubo oscillator.

  • Keywords

backward error analysis modified equations strong convergence stochastic numerical integrator

  • AMS Subject Headings

65C30 60H35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-1, author = {}, title = {Strong Backward Error Analysis for Euler-Maruyama Method}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {1--21}, abstract = {Backward error analysis is an important tool to study long time behavior of numerical methods. The main idea of it is to use perturbed equations, namely modified equations, to represent the numerical solutions. Since stochastic backward error analysis has not been well developed so far. This paper investigates the stochastic modified equation and backward error analysis for Euler-Maruyama method with respect to strong convergence are built up. Like deterministic case, stochastic modified equations, expressed as formal series, do not converge in general. But there exists the optimal truncation of the series such that the one step error of the modified equations is sub-exponentially small with respect to time step. Moreover, the result of stochastic backward error analysis is used to study the error growth of the Euler-Maruyama method on Kubo oscillator.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/423.html} }
TY - JOUR T1 - Strong Backward Error Analysis for Euler-Maruyama Method JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 21 PY - 2016 DA - 2016/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/423.html KW - backward error analysis KW - modified equations KW - strong convergence KW - stochastic numerical integrator AB - Backward error analysis is an important tool to study long time behavior of numerical methods. The main idea of it is to use perturbed equations, namely modified equations, to represent the numerical solutions. Since stochastic backward error analysis has not been well developed so far. This paper investigates the stochastic modified equation and backward error analysis for Euler-Maruyama method with respect to strong convergence are built up. Like deterministic case, stochastic modified equations, expressed as formal series, do not converge in general. But there exists the optimal truncation of the series such that the one step error of the modified equations is sub-exponentially small with respect to time step. Moreover, the result of stochastic backward error analysis is used to study the error growth of the Euler-Maruyama method on Kubo oscillator.
J. Deng. (1970). Strong Backward Error Analysis for Euler-Maruyama Method. International Journal of Numerical Analysis and Modeling. 13 (1). 1-21. doi:
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