Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912007062552576 |
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| author | Paikaray, Prit Pritam Beuria, Sanghamitra Parida, Nigam Chandra |
| author_facet | Paikaray, Prit Pritam Beuria, Sanghamitra Parida, Nigam Chandra |
| contents | This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of the proposed method for stochastic Volterra integral equations with Lipschitz functions are presented. Numerous examples with available analytical solutions demonstrate that the proposed method solves linear stochastic Volterra integral equations more precisely than existing techniques. In addition, the numerical behaviour of the method for a problem with no known analytical solution is demonstrated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_00823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function Paikaray, Prit Pritam Beuria, Sanghamitra Parida, Nigam Chandra Numerical Analysis Probability 60H05, 60H35, 65C30 This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of the proposed method for stochastic Volterra integral equations with Lipschitz functions are presented. Numerous examples with available analytical solutions demonstrate that the proposed method solves linear stochastic Volterra integral equations more precisely than existing techniques. In addition, the numerical behaviour of the method for a problem with no known analytical solution is demonstrated. |
| title | Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function |
| topic | Numerical Analysis Probability 60H05, 60H35, 65C30 |
| url | https://arxiv.org/abs/2305.00823 |