Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910913215332352 |
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| author | Asadzade, Javad A. Mahmudov, Nazim I. |
| author_facet | Asadzade, Javad A. Mahmudov, Nazim I. |
| contents | This manuscript examines the problem of nonlinear stochastic fractional neutral integro-differential equations with weakly singular kernels. Our focus is on obtaining precise estimates to cover all possible cases of Abel-type singular kernels. Initially, we establish the existence, uniqueness, and continuous dependence on the initial value of the true solution, assuming a local Lipschitz condition and linear growth condition. Additionally, we develop the Euler-Maruyama method for the numerical solution of the equation and prove its strong convergence under the same conditions as the well-posedness. Moreover, we determine the accurate convergence rate of this method under global Lipschitz conditions and linear growth conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel Asadzade, Javad A. Mahmudov, Nazim I. Numerical Analysis Classical Analysis and ODEs This manuscript examines the problem of nonlinear stochastic fractional neutral integro-differential equations with weakly singular kernels. Our focus is on obtaining precise estimates to cover all possible cases of Abel-type singular kernels. Initially, we establish the existence, uniqueness, and continuous dependence on the initial value of the true solution, assuming a local Lipschitz condition and linear growth condition. Additionally, we develop the Euler-Maruyama method for the numerical solution of the equation and prove its strong convergence under the same conditions as the well-posedness. Moreover, we determine the accurate convergence rate of this method under global Lipschitz conditions and linear growth conditions. |
| title | Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel |
| topic | Numerical Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.15407 |