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Mathematics > Numerical Analysis
Title: Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel
(Submitted on 27 Jan 2024 (v1), last revised 25 Apr 2024 (this version, v2))
Abstract: 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.
Submission history
From: Javad Asadzade [view email][v1] Sat, 27 Jan 2024 13:37:57 GMT (137kb,D)
[v2] Thu, 25 Apr 2024 05:42:24 GMT (639kb,D)
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