期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 344, 期 -, 页码 108-126出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.04.078
关键词
Nonlinear time-fractional fourth-order problem; WSGD scheme; LDG method; High-order scheme; Caputo fractional derivative
资金
- National Natural Science Foundation of China [11661058, 11361035, 11501311]
- Natural Science Fund of Inner Mongolia Autonomous Region [2014BS0101]
- Scientific Research Projection of Higher Schools of Inner Mongolia [NJZZ12011, NJZY14013]
In this article, a fully discrete local discontinuous Galerkin (LDG) method with high-order temporal convergence rate is presented and developed to look for the numerical solution of nonlinear time-fractional fourth-order partial differential equation (PDE). In the temporal direction, for approximating the fractional derivative with order alpha is an element of(0, 1), the weighted and shifted Grunwald difference (WSGD) scheme with second-order convergence rate is introduced and for approximating the integer time derivative, two step backward Euler method with second-order convergence rate is used. For the spatial direction, the LDG method is used. For the numerical theories, the stability is derived and a priori error results are proved. Further, some error results and convergence rates are calculated by numerical procedure to illustrate the effectiveness of proposed method. (C) 2017 Elsevier Inc. All rights reserved.
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