An Efficient Iteration Method for Toeplitz-Plus-Band Triangular Systems Generated from Fractional Ordinary Differential Equation

摘要

It is time consuming to numerically solve fractional differential equations. The fractional ordinary differential equations may produce Toeplitz-plus-band triangular systems. An efficient iteration method for Toeplitz-plus-band triangular systems is presented withOMlogMcomputational complexity andOMmemory complexity in this paper, compared with the regular solution withOM2computational complexity andOM2memory complexity.Mis the discrete grid points. Some methods such as matrix splitting, FFT, compress memory storage and adjustable matrix bandwidth are used in the presented solution. The experimental results show that the presented method compares well with the exact solution and is 4.25 times faster than the regular solution.