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Approximate solution for stochastic Volterra integral equations with constant delay

Published: 22 August 2024 Publication History

Abstract

The study proposes a novel approach that uses block pulse functions (BPFs) with constant delays to approximate stochastic Volterra integral equations (SVIEs). The method simplifies the problem by converting delay-containing SVIEs into algebraic ones using operational matrices of BPFs. This approach is easily solvable and effective, as shown through numerical examples.

References

[1]
Dawood, H.K, 2019, Computational block-pulse functions method for solving Volterra integral equations with delay. J. Univ. Babylon, 27, 32–43.
[2]
Kasumo, C, 2020, On the approximate solutions of linear Volterra integral equations of the first kind, Appl. Math. Sci. 14(3), 141–153.
[3]
Maleknejad, K., Torabi, P., Sauter, S, 2016, Numerical solution of a non-linear Volterra integral equation, Vietnam J. Math. 14(1), 5–28.
[4]
Babolian, E., Masouri, Z., 2008, Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions, J. Comput. Appl. Math. 220(1–2), 51–57.
[5]
Gutleb,T.S, Olver, S., 2019, A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle, SIAM J. Numer. Anal. 58(3),1993-2018.
[6]
Maleknejad, K, Mahdiani, K. Solving nonlinear mixed Volterra-Fredholm integral equations with two dimensional block-pulse functions using direct method, Communications in Nonlinear Science and Numerical Simulation}, https://doi.org/10.1016/j.cnsns.2010.12.036.
[7]
Rabbani, M.Nouri, K. 2010, Solution of integral equations by using block-pulse functions, Mathematical Sci.: Q. J. (MSQJ), 2010,4(1):39.
[8]
Kutorzi E.Y, Y. Zhang, Y. Shi, 2024, Numerical Solution for Stochastic Volterra-Fredholm Integral Equations with Delay Arguments, Acta polytechnica, 64 (2): 128-141, 2024.
[9]
Quanxin Zhu and Tingwen Huang, 2020, Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion, Systems & Control Letters, 140(2020) 104699.
[10]
M. Nouri and K. Maleknejad, 2016, Numerical Solution of Delay Integral Equations by Using Block Pulse Functions Arises in Biological Sciences, International J. of Mathematical Modelling & Computations Vol.06, No.03 (2016), pp. 221-232.
[11]
L. Wan, Q. Zhou, 2019, Stochastic Lotka–Volterra model with infinite delay, Statist. Probab. Lett., 79 (2009), pp. 698-706.
[12]
K.L. Cooke, J.A. Yorke, 1973, Some equations modelling growth processes and gonorrhea epidemics, Math. Biosci., 16 (1973) 75-101.
[13]
K.L. Cooke, 1979, An epidemic equation with immigration, Math. Biosci., 29 (1976) 135-158.
[14]
H.L. Smith, 1977, On periodic solutions of a delay integral equation modelling epidemics, J. Math. Biol., 4 (1977) 69-80.
[15]
Z.H. Jiang, W. Schaufelberger,1992, Block Pulse Functions and their Applications in Control Systems, Springer-Verlag, 1992.
[16]
G. Prasada Rao, 1983, Piecewise Constant Orthogonal Functions and Their Application to Systems and Control, Springer, Berlin, 1983.
[17]
Stenger, F.1993, Numerical methods based on sinc and analytic functions, Springer Verlag, New York, 1993.
[18]
J. Gao, H. Liang, S. Ma, 2019, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Appl. Math. Comput., 348, 385-398 (2019).
[19]
F. Z. Geng, Piecewise reproducing kernel-based symmetric collocation approach for linear stationary singularly perturbed problems, AIMS Mathematics, 2020, 5(6): 6020-6029.
[20]
Samar, M, Kutorzi, E,Y, Zhu, X, 2023, Numerical solution of Nonlinear backward stochastic Volterra integral equations, Axioms, 2023, 12, 888.
[21]
M. Khodabina, K. Maleknejada, M. Rostami, M. Nouri, 2012, Numerical approach for solving stochastic Volterra-Fredholm integral equations by stochastic operational matrix, Computers and Mathematics with Applications, 64, 2012, 1903-1913.

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    ICMAI '24: Proceedings of the 2024 9th International Conference on Mathematics and Artificial Intelligence
    May 2024
    134 pages
    ISBN:9798400717284
    DOI:10.1145/3670085
    Publication rights licensed to ACM. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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    Published: 22 August 2024

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    • Major Fundamental Research Project of Shandong Province of China
    • y National Key R&D Program of China

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