Stability and convergence of multistep schemes for 1D and 2D fractional model with nonlinear source term

摘要

Stable multistep schemes based on Caputo fractional derivative approximation are pre-sented for solving 1D and 2D nonlinear fractional model arising from dielectric media. We approximate Caputo fractional derivatives in time with a multistep scheme of order O(tau(3-alpha)) & O(tau(3-beta)), 1 < beta