Numerical Approximation of Stochastic Volterra-Fredholm Integral Equation using Walsh Function

Authors

  • Prit Pritam Paikaray Department of Mathematics, College of Basic Science and Humanities, Odisha University of Agriculture & Technology, Bhubaneswar 751003, Odisha, India https://orcid.org/0000-0003-3028-3788
  • Sanghamitra Beuria Department of Mathematics, College of Basic Science and Humanities, Odisha University of Agriculture & Technology, Bhubaneswar 751003, Odisha, India https://orcid.org/0000-0003-3913-7517
  • Nigam Chandra Parida Department of Mathematics, College of Basic Science and Humanities, Odisha University of Agriculture & Technology, Bhubaneswar 751003, Odisha, India https://orcid.org/0009-0006-1918-1739

DOI:

https://doi.org/10.26713/cma.v14i5.2313

Keywords:

Stochastic Volterra-Fredholm integral equation, Brownian motion, Itô integral, Walsh approximation, Lipschitz condition

Abstract

In this paper, a computational method is developed to find an approximate solution to the stochastic Volterra-Fredholm integral equation using the Walsh function approximation and its operational matrix. Moreover, convergence and error analysis of the method is carried out to strengthen its validity. Furthermore, the method is numerically compared to the block pulse function method and the Haar wavelet method for some non-trivial examples.

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References

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Published

16-04-2024
CITATION

How to Cite

Paikaray, P. P., Beuria, S., & Parida, N. C. (2024). Numerical Approximation of Stochastic Volterra-Fredholm Integral Equation using Walsh Function. Communications in Mathematics and Applications, 14(5), 1603–1613. https://doi.org/10.26713/cma.v14i5.2313

Issue

Vol. 14 No. 5 (2023)

Section

Research Article

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