Finite element method combined with second-order time discrete scheme for nonlinear fractional Cable equation
School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, China
2 School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, 010070, Hohhot, China
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Accepted: 25 January 2016
Published online: 21 March 2016
In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time , a second-order two step scheme with -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order ( in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in -norm with are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016