Numerical Approximation for a Stochastic Caputo Fractional Differential Equation with Multiplicative Noise
Year: 2025
Type: article
Abstract: We investigate a numerical method for approximating stochastic Caputo fractional differential equations driven by multiplicative noise. The nonlinear functions f and g are assumed to satisfy the global Lipschitz conditions as well as the linear growth conditions. The noise is approximated by a piecewise constant function, yielding a regularized stochastic fractional differential equation. We prove that the error between the exact solution and the solution of the regularized equation converges in the L2((0,T)×Ω) norm with an order of O(Δtα−1/2), where α∈(1/2,1] is the order of the Caputo fractional derivative, and Δt is the time step size. Numerical experiments are provided to confirm that the simulation results are consistent with the theoretical convergence order.
Source: Mathematics
DOI: 10.3390/math13172835
Authors: James Hoult, Yubin Yan
Institution: University of Chester
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4413958150