Open AccessSome second-order š schemes combined with finite element method for nonlinear fractional cable equation
Author(s) -
Yang Liu,
Yanwei Du,
Hong Li,
Fawang Liu,
Yajun Wang
Publication year - 2018
Publication title -
numerical algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.981
H-Index - 64
eISSN - 1572-9265
pISSN - 1017-1398
DOI - 10.1007/s11075-018-0496-0
Subject(s) - mathematics , discretization , galerkin method , finite element method , nonlinear system , norm (philosophy) , fractional calculus , theory of computation , mathematical analysis , rate of convergence , numerical analysis , order (exchange) , stability (learning theory) , discontinuous galerkin method , convergence (economics) , algorithm , physics , channel (broadcasting) , electrical engineering , finance , quantum mechanics , machine learning , economic growth , political science , computer science , law , economics , thermodynamics , engineering
In this article, some second-order time discrete schemes covering parameter combined with Galerkin finite element (FE) method are proposed and analyzed for looking for the numerical solution of nonlinear cable equation with time fractional derivative. At time tkā, some second-order schemes combined with weighted and shifted GrĆ¼nwald difference (WSGD) approximation of fractional derivative are considered to approximate the time direction, and the Galerkin FE method is used to discretize the space direction. The stability of second-order schemes is derived and the second-order time convergence rate in L2-norm is proved. Finally, some numerical calculations are implemented to indicate the feasibility and effectiveness for our schemes.
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