Yan, YubinKhan, MonzorulFord, Neville J.2017-09-292017-09-292018-01-11Yan, Y. , Khan, M., & Ford, N. J. (2018). An analysis of the modified L1 scheme for time-fractional partial differential equations with nonsmooth data. SIAM Journal on Numerical Analysis (SINUM), 56(1), 210-227. https://doi.org/10.1137/16M10942570036-142910.1137/16M1094257http://hdl.handle.net/10034/620639First Published in SIAM Journal on Numerical Analysis (SINUM), 56(1), 2018, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.We introduce a modified L1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous cases. Jin \et (2016, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data, IMA J. of Numer. Anal., 36, 197-221) established an $O(k)$ convergence rate for the L1 scheme for smooth and nonsmooth initial data for the homogeneous problem, where $k$ denotes the time step size. We show that the modified L1 scheme has convergence rate $O(k^{2-\alpha}), 0< \alpha <1$ for smooth and nonsmooth initial data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the numerical results are consistent with the theoretical results.enhttp://creativecommons.org/licenses/by-nc/4.0/Time fractional partial differential equationsCaputo fractional derivativeError estimatesLaplace transformArticle1095-7170SIAM Journal on Numerical Analysis (SINUM)