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Solving system of linear Stratonovich Volterra integral equations via modification of hat functions

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  • Mirzaee, Farshid
  • Hadadiyan, Elham

Abstract

This paper proposes an efficient method for solving system of linear Stratonovich Volterra integral equations. Stochastic operational matrix of modification of hat functions (MHFs) is determined. By using MHFs and their stochastic operational matrix of integration, a system of linear Stratonovich Volterra integral equations can be reduced to a linear system of algebraic equations. Thus we can solve the problem by direct methods. Also, we prove that the rate of convergence is O(h3). Efficiency of this method and good degree of accuracy are confirmed by numerical examples.

Suggested Citation

  • Mirzaee, Farshid & Hadadiyan, Elham, 2017. "Solving system of linear Stratonovich Volterra integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 254-264.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:254-264
    DOI: 10.1016/j.amc.2016.08.016
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    References listed on IDEAS

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    1. Harnett, Daniel & Nualart, David, 2012. "Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3460-3505.
    2. Maillard-Teyssier, Laurence, 2006. "Stratonovich covariant differential equation with jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1860-1875, December.
    3. Mirzaee, Farshid & Hadadiyan, Elham, 2016. "Numerical solution of Volterra–Fredholm integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 110-123.
    4. Bardina, Xavier & Jolis, Maria, 2000. "Weak convergence to the multiple Stratonovich integral," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 277-300, December.
    5. Arnold, Ludwig & Imkeller, Peter, 1996. "Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 19-54, March.
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    Cited by:

    1. He, Lingyun & Banihashemi, Seddigheh & Jafari, Hossein & Babaei, Afshin, 2021. "Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).

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