A Meshless Method for the Numerical Solution of Fractional Stochastic Integro-Differential Equations Based on the Moving Least Square Approach

Recently, more and more researchers focus on stochastic fractional equations due to their applicability to describe the memory and randomness of many noise systems problems. In the current work, we develop a meshless approach based on moving least square approximation (MLS) to solve stochastic fract...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2023-06, Vol.9 (3), Article 27
Main Authors: El Majouti, Zahra, Taghizadeh, Elham, El Jid, Rachid
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Basis functions
Computational mathematics
Computational Science and Engineering
Differential equations
Exact solutions
Finite element method
Fractional calculus
Least squares
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Meshless methods
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Randomness
Theoretical
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Summary:Recently, more and more researchers focus on stochastic fractional equations due to their applicability to describe the memory and randomness of many noise systems problems. In the current work, we develop a meshless approach based on moving least square approximation (MLS) to solve stochastic fractional integro-differential equations (SFIDEs). To establish the scheme; we consider the composite Gauss-Legendre integration rule for computing the singular-fractional integral and the Riemann sum for estimating It o ^ integral. We have also compared different basis in terms of CPU time. The error bound of the method is provided. The major accuracy of this approach is that the approximate solutions converge more quickly to the exact solutions by choosing a small number of basis functions and nodes, then the computational cost of the moment matrix is reduced. Several numerical test problems are presented. Comparing the results obtained with other methods confirm the efficiency of the proposed scheme.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-023-01521-7