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An efficient meshless method to approximate semi-linear stochastic evolution equations

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Abstract

In this article, we are concerned with meshless methods to approximate and simulate the solution of semi-linear stochastic evolution equations. We first study the asymmetric Kansa method and then consider its regularized form. Kansa method is an efficient approach that is easy to implement and adapt and has sufficient accuracy and approximation power. We employ Karhunen–Loéve expansion for having faster and better simulations for the stochastic part. The absolute error, standard deviation, root mean square error, and CPU times for showing the accuracy and speed of our methodology are calculated. From the numerical analysis view, the stability of this methodology for time-dependent problems is investigated by numerical factors in the computational part. Experimentally, the performance of both presented methods is more significant, and proportionally they have better results to previous work in this subject.

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Acknowledgements

The authors are very grateful to the two reviewers for carefully reading the paper and for their constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

    Mahdi Jalili & Rezvan Salehi

  2. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran

    Mehdi Dehghan

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  1. Mahdi Jalili
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Correspondence to Rezvan Salehi.

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Jalili, M., Salehi, R. & Dehghan, M. An efficient meshless method to approximate semi-linear stochastic evolution equations. Engineering with Computers 40, 61–90 (2024). https://doi.org/10.1007/s00366-022-01770-y

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