In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analy...In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically validated.The contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder accurate.Several numerical examples are provided to verify the theoretical statement.展开更多
基金supported by the Fujian Alliance of Mathematics(Grant No.2024SXLMMS03)by the Natural Science Foundation of Fujian Province of China(Grant No.2022J01338)+4 种基金supported by the NSFC(Grant Nos.12361083,62341115)by the Foundation of Guizhou Science and Technology Department(Grant No.QHKJC-ZK[2024]YB497)by the Natural Science Research Project of Department of Education of Guizhou Province(Grant No.QJJ2023012)by the Science Research Fund Support Project of the Guizhou Minzu University(Grant No.GZMUZK[2023]CXTD05)supported by the NSFC(Grant No.12371408).
文摘In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically validated.The contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder accurate.Several numerical examples are provided to verify the theoretical statement.
