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Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations

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Abstract

In various fields of science and engineering, such as financial mathematics, mathematical physics models, and radiation transfer, stochastic integral equations are important and practical tools for modeling and describing problems. Due to the existence of random factors, we face a fundamental problem in solving stochastic integral equations, and that is the lack of analytical solutions or the great complexity of these solutions. Therefore, finding an efficient numerical solution is essential. In this paper, we intend to propose and study a new method based on the Floater-Hormann interpolation and the spectral collocation method for linear and nonlinear stochastic Itô-Volterra integral equations (SVIEs). The Floater-Hormann interpolation offers an approximation regardless of the distribution of the points. Therefore, this method can be mentioned as a meshless method. The presented method reduces SVIEs under consideration into a system of algebraic equations that can be solved by the appropriate method. We presented an error bound to be sure of the convergence and reliability of the method. Finally, the efficiency and the applicability of the present scheme are investigated through some numerical experiments.

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Acknowledgements

The authors would like to state our appreciation to the editor and referees for their costly comments and constructive suggestions which have improved the quality of the current paper.

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Authors and Affiliations

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

    Farshid Mirzaee, Shiva Naserifar & Erfan Solhi

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

Conceptualization: Farshid Mirzaee and Shiva Naserifar. Formal analysis: Farshid Mirzaee and Shiva Naserifar. Investigation: Farshid Mirzaee and Erfan Solhi. Methodology: Erfan Solhi and Shiva Naserifar. Validation: Farshid Mirzaee and Shiva Naserifar. Visualization: Farshid Mirzaee and Erfan Solhi. Writing—original draft: Erfan Solhi and Shiva Naserifar.

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Correspondence to Farshid Mirzaee.

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Mirzaee, F., Naserifar, S. & Solhi, E. Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations. Numer Algor 94, 275–292 (2023). https://doi.org/10.1007/s11075-023-01500-5

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