The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference oper...The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L<sub>2</sub>-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.展开更多
基金supported by the National Natural Science Foundation of China(21872104,51908408,21872163,and 22072090)the National Key Research and Development Program of China(2017YFB0602200,2020YFA0211000,and 2020YFA0211003)+3 种基金the Innovative Research Team of Tianjin Municipal Education Commission(TD13-5008)Tianjin Science and Technology Planning Project(21ZYQCSY00050)the support from the Natural Science Foundation of Tianjin for Distinguished Young Scholar(20JCJQJC00150)the support from the Tencent Foundation through the XPLORER PRIZE。
文摘The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L<sub>2</sub>-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.
