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J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p> Numerical approximation for a linearized time fractional KdV equation with initial singularity using [Formula: see text] scheme on graded mesh is considered. It is proved that the [Formula: see text] scheme can attain order [Formula: see text] convergence rate with appropriate choice of the grading parameter, where [Formula: see text] [Formula: see text] is the order of temporal Caputo fractional derivative. A fully discrete spectral scheme is constructed combing a Petrov\u2013Galerkin 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. <\/jats:p>","DOI":"10.1142\/s179396231941006x","type":"journal-article","created":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T03:20:56Z","timestamp":1540524056000},"page":"1941006","source":"Crossref","is-referenced-by-count":17,"title":["L1 scheme on graded mesh for the linearized time fractional KdV equation with initial singularity"],"prefix":"10.1142","volume":"10","author":[{"given":"Hu","family":"Chen","sequence":"first","affiliation":[{"name":"Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100194, P. R. China"}]},{"given":"Xiaohan","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China"}]},{"given":"Jincheng","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450045, P. R. China"}]},{"given":"Tao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China"}]},{"given":"Yifa","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China"},{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. 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