A new difference scheme for fractional cable equation and stability analysis

Abstract

We consider the fractional cable equation. For solution of fractional Cable equation involving Caputo fractional derivative, a new difference scheme is constructed based on Crank Nicholson difference scheme. We prove that the proposed method is unconditionally stable by using spectral stability technique.

A numerical approach for a class of time-fractional reaction–diffusion equation through exponential B-spline method

“…Also, the results in these tables demonstrate the superiority of the present method over the method in (Zhang and Yang 2018). Comparison of numerical results in Table 3 for example 2 also show that present method gives more accurate results than the method given in (Karatay and Kale 2015). The L 2 errors with different fractional orders in spatial direction for the problems in examples 2, 3, 4, 5, and 6 are obtained by the proposed method, and reported in Tables 4, 6, 8, 10, and 12, respectively.…”

Numerical simulation of time fractional Cable equations and convergence analysis

“…Liu and Yang [15], proposed two new implicit numerical methods with convergence analysis for the fractional Cable equation. Ibrahim and Nurdane [16] constructed a new difference scheme based on Crank-Nicholson difference scheme for solution of fractional Cable equation involving Caputo fractional derivative. Bu [17,18] considered finite element multigrid method for time fractional advection diffusion equations.…”