The cubic trigonometric B-spline collocation method for the time-fractional stochastic Advection-Diffusion equation

Yazdani Cherati, Allahbakhsh; Azimi, Zohre

doi:10.22075/ijnaa.2022.7182

The cubic trigonometric B-spline collocation method for the time-fractional stochastic Advection-Diffusion equation

Document Type : Research Paper

Authors

Allahbakhsh Yazdani Cherati

Zohre Azimi

Department of Applied Mathematics, Faculty of Mathematical Science, University of Mazandaran, Babolsar, Iran

10.22075/ijnaa.2022.7182

Abstract

The ultimate goal of this performance study is to provide a proposed scheme for solving the time-fractional stochastic advection-diffusion equation (TFSADE) of order $\alpha (0\le \alpha <1)$. In this proposed scheme, we utilize an approach based on cubic trigonometric B-spline collocation methods (CTBSCM). In this study, we replace the existing fractional derivative with the fractional Caputo derivative for time discretization and then replace the first and second derivatives of the equation using cubic trigonometric B-spline functions for spatial discretization. Applying this proposed scheme to TFSADE causes the equation to reduce to the linear system. In the end, the examples show that the order of convergence of the proposed method is $O(\tau ^{2-\alpha}+h^2)$ where $h$ and $\tau$ are the spatial and time step lengths, respectively.

Keywords

Fractional stochastic equation

Cubic trigonometric B-spline

Brownian motion

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