Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with ap...Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with appropriate choice of the grading parameter,whereα(0<α<1)is the order of temporal Caputo fractional derivative.A fully discrete spectral scheme is constructed combing a Petrov-Galerkin spectral method for the spatial discretization,and its stability and convergence are theoretically proved.Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis.展开更多
基金The work of Hu Chen is supported in part by NSF of China(No.11801026)and China Postdoctoral Science Foundation Under No.2018M631316the work of Xiaohan Hu and Yifa Tang is supported in part by NSF of China(No.11771438)+3 种基金the work of Jincheng Ren is supported in part by NSF of China(No.11601119)sponsored by Program for HASTIT(No.18HASTIT027)Young talents Fund of HUELthe work of Tao Sun is supported in part by NSF of China(No.11401380).
文摘Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with appropriate choice of the grading parameter,whereα(0<α<1)is the order of temporal Caputo fractional derivative.A fully discrete spectral scheme is constructed combing a Petrov-Galerkin spectral method for the spatial discretization,and its stability and convergence are theoretically proved.Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis.
