Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations
The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this p...
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| Published in: | Numerical algorithms Vol. 99; no. 2; pp. 809 - 835 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
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Springer US
01.06.2025
Springer Nature B.V |
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| ISSN: | 1017-1398, 1572-9265 |
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| Abstract | The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique. |
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| AbstractList | The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique. |
| Author | Zeghdane, Rebiha |
| Author_xml | – sequence: 1 givenname: Rebiha surname: Zeghdane fullname: Zeghdane, Rebiha email: rebiha.zeghdane@univ-bba.dz organization: Mathematical Analysis and Applications Laboratory, Department of Mathematics, Faculty of Mathematics and Informatics, Mohamed El Bachir El Ibrahimi University of Bordj Bou Arreridj |
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| Cites_doi | 10.1016/j.cam.2019.112440 10.1016/j.mcm.2011.08.053 10.1016/j.jcp.2015.05.051 10.1016/j.camwa.2012.03.042 10.1016/j.cam.2018.09.040 10.1002/mma.5890 10.1016/j.camwa.2011.10.079 10.1016/j.cam.2016.04.012 10.1016/j.mcm.2006.07.017 10.1016/j.apnum.2020.11.013 10.1137/0114039 10.1186/s13662-019-2096-2 10.1007/978-94-015-8455-5 10.1007/978-3-031-22430-0_1 10.1016/j.aej.2013.02.004 10.1016/j.cam.2017.09.035 10.1016/j.rinam.2022.100260 10.1515/math-2016-0027 10.1016/j.amc.2014.09.047 10.1016/j.jde.2008.02.019 10.1007/978-3-662-12616-5 10.1086/260062 10.1007/BF00773344 10.1007/s00009-015-0642-z 10.1016/j.jcp.2014.03.064 10.1108/MMMS-04-2018-0075 10.1137/090747920 10.1080/07362994.2020.1858873 10.1016/j.camwa.2006.05.030 10.1016/j.apm.2011.07.061 |
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| Keywords | Itô integral Picard iteration Quadrature formula Numerical solution Stochastic differential equation |
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| SubjectTerms | Algebra Algorithms Approximation Banach spaces Computer Science Integral equations Iterative methods Numeric Computing Numerical Analysis Original Paper Picard iterations Quadratures Random variables Stochastic models Theory of Computation Volterra integral equations |
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| Title | Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations |
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