Abstract
In this paper, a stochastic space fractional advection diffusion equation of Itô type with one-dimensional white noise process is presented. The fractional derivative is defined in the sense of Caputo. A stochastic compact finite difference method is used to study the proposed model numerically. Stability analysis and consistency for the stochastic compact finite difference scheme are proved. Two test examples are given to test the performance of the proposed method. Numerical simulations show that the results obtained are compatible with the exact solutions and with the solutions derived in the literature.
Highlights
Many physical phenomena are simulated using mathematical models that lead to partial differential deterministic equations (PDEs)
Due to a lack of data on parameters and initial data, the behavior of the system might be far away from the ideal deterministic representation. To counter this lack of information and make a system explanation more practical, one adds random inputs that can be random variables or stochastic processes. This leads to stochastic partial differential equations (SPDEs)
We introduced a stochastic fractional advection-diffusion equation (SFADE), which can be considered as a generalization of the classical Advection-diffusion equation (ADE) with a one-dimensional multiplicative white noise process, replacing the second and first-order space derivatives with the Caputo fractional-order derivative α ∈
Summary
Many physical phenomena are simulated using mathematical models that lead to partial differential deterministic equations (PDEs). Roth [9] used an explicit finite difference method to approximate a solution of some stochastic hyperbolic equations.
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