An efficient iteration method for Toeplitz-plus-band triangular systems generated from fractional ordinary differential equation
Summary: 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 with \(O \left(M \text{l} \text{o} \text{g} \left(M\right)\right)\) computational complexity and \(O \left(M\right)\) memory complexity in this paper, compared with the regular solution with \(O \left(M^2\right)\) computational complexity and \(O \left(M^2\right)\) memory complexity. \(M\) is 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.
scientific article; zbMATH DE number 7015885
scientific article