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Meshless local numerical procedure based on interpolating moving least squares approximation and exponential time differencing fourth-order Runge–Kutta (ETDRK4) for solving stochastic parabolic interface problems

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Abstract

The main propose of this investigation is to develop an interpolating meshless numerical procedure for solving the stochastic parabolic interface problems. The present numerical algorithm is constructed from the interpolating moving least squares (ISMLS) approximation. At first, the space variable has been discretized by using the ISMLS approximation. Then, the PDE reduces to the system of nonlinear ODEs. In the next, to achieve a high-order numerical formula, we employ a fourth-order time discrete scheme that is well-known as the explicit fourth-order exponential time differencing Runge-Kutta method (ETDRK4). This method is simple and has acceptable accuracy for solving the considered problems. Several examples with adequate intricacy are examined to check the new numerical procedure.

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Acknowledgements

The authors are grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.

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  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Mostafa Abbaszadeh & Mehdi Dehghan

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  1. Mostafa Abbaszadeh
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  2. Mehdi Dehghan
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Correspondence to Mostafa Abbaszadeh.

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Abbaszadeh, M., Dehghan, M. Meshless local numerical procedure based on interpolating moving least squares approximation and exponential time differencing fourth-order Runge–Kutta (ETDRK4) for solving stochastic parabolic interface problems. Engineering with Computers 38 (Suppl 1), 71–91 (2022). https://doi.org/10.1007/s00366-020-01057-0

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