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Enhanced moving least squares method for solving the stochastic fractional Volterra integro-differential equations of Hammerstein type

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Abstract

One of the challenging and practical issues that have recently attracted the attention of researchers is stochastic equations. One of the important categories in stochastic equations is the stochastic fractional integro-differential equations (SFIDEs), which are practical tools for modeling many phenomena. In this study, we aim to derive a novel numerical method based on the meshless enhanced moving least squares (EMLS) and spectral method for solving SFIDEs, which transform the intended problem to a nonlinear system of algebraic equations. Thus, the complexity of solving the mentioned problem is reduced significantly. Also, we give an error estimate which will be useful in estimating the error of approximate solutions for the problems that we do not have information about their exact solutions. Illustrative numerical examples are also given to clarify the performance and accuracy of the new method. This method is far from computational complexity compared to other methods. Also, obtaining acceptable accuracy by choosing a small number of interpolation nodes and basis functions is one of the innovations of this work.

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Acknowledgements

The authors would like to express our very great appreciation to the editor and anonymous reviewers for their valuable comments and constructive suggestions which have helped to improve the quality and presentation of this paper

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Authors and Affiliations

  1. Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, 65719-95863, Iran

    Erfan Solhi, Farshid Mirzaee & Shiva Naserifar

Authors
  1. Erfan Solhi
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  2. Farshid Mirzaee
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  3. Shiva Naserifar
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Contributions

Conceptualization, Farshid Mirzaee and Erfan Solhi; formal analysis, Erfan Solhi and Shiva Naserifar; investigation, Erfan Solhi and Farshid Mirzaee; methodology, Erfan Solhi and Shiva Naserifar; validation, Erfan Solhi and Farshid Mirzaee; visualization, Erfan Solhi and Farshid Mirzaee; writing—original draft, Erfan Solhi and Shiva Naserifar.

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Correspondence to Farshid Mirzaee.

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Solhi, E., Mirzaee, F. & Naserifar, S. Enhanced moving least squares method for solving the stochastic fractional Volterra integro-differential equations of Hammerstein type. Numer Algor 95, 1921–1951 (2024). https://doi.org/10.1007/s11075-023-01633-7

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  • DOI: https://doi.org/10.1007/s11075-023-01633-7

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