Fast L sigma fractional alternating-Direction implicite schemed

Abstract

The fractional derivatives has singuler kernel and it cause massive computational cost. In this research, to solve given fractional partial differential equation, fast algorithm that solves a time fractional part of PDE and alternating-direction implicit sheme which handles space part are combined. The fast algorithm is based on the L2-1sigma scheme and the SOE method, thus suggested scheme has O(\delta t^2) order convergence rate and computational cost is O(nlog2 n). The effectiveness of the proposed scheme will be presented by numerical examples.