报告题目 (Title)：High-Order Stable Computational Algorithm for Space-Time Fractional Stochastic Nonlinear Diffusion Wave Model (时空分数阶随机非线性扩散波模型的高阶稳定计算算法)

报告人 (Speaker)： Anant Pratap Singh 博士（Indian Institute of Technology (Banaras Hindu University) 大学）

报告时间 (Time)：2024年5月21日 (周二) 15:00

报告地点 (Place)：校本部GJ403

邀请人(Inviter)：李常品、蔡敏

主办部门：理学院数学系

报告摘要：In the current work a numerical method is developed and examined for the space–time fractional stochastic nonlinear diffusion wave model. The implicit numerical scheme is designed by embedding the matrix transform approach for discretizing the Riesz-space fractional derivative, and via incorporating (3 − α) order approximation to the Caputo-fractional derivative in the temporal direction. Further, Taylor's series method is utilized to linearize the nonlinear source term, and has been efficiently employed to compute the solution of a class of nonlinear fractional diffusion wave equation. We demonstrate that the implicit scheme converges with β-order in space and (3−α) order in time. The theoretical investigation of the unconditional stability of the implicit scheme and the optimal error estimates in the temporal-spatial direction are conducted. Moreover, the consistency and high efficacy of the proposed numerical algorithms are further supported by several numerical tests, which shows that the designed numerical technique is easy to implement and in sync with the theoretical investigation.