Abstract and Applied Analysis

A Simplified Milstein Scheme for SPDEs with Multiplicative Noise

B. Ghayebi and S. M. Hosseini

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Abstract

This paper deals with a research question raised by Jentzen and Röckner (A Milstein scheme for SPDEs, arXiv:1001.2751v4 (2012)), whether the exponential term in their introduced scheme can be replaced by a simpler mollifier. This replacement can lead to more simplification and computational reduction in simulation. So, in this paper, we essentially replace the exponential term with a Padé approximation of order 1 and denote the resulting scheme by simplified Milstein scheme. The convergence analysis for this scheme is carried out and it is shown that even with this replacement the order of convergence is maintained, while the resulting scheme is easier to implement and slightly more efficient computationally. Some numerical tests are given that confirm the order of accuracy and also computational cost reduction.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 140849, 15 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277355

Digital Object Identifier
doi:10.1155/2014/140849

Mathematical Reviews number (MathSciNet)
MR3248844

Zentralblatt MATH identifier
07021796

Citation

Ghayebi, B.; Hosseini, S. M. A Simplified Milstein Scheme for SPDEs with Multiplicative Noise. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 140849, 15 pages. doi:10.1155/2014/140849. https://projecteuclid.org/euclid.aaa/1412277355


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