Symmetric modified AOR method to solve systems of linear equations

Abstract

We propose a class of symmetric modified accelerated overrelaxation (SMAOR) methods for solving large sparse linear systems. The convergence region of the method has been investigated. Numerical examples indicate that the SMAOR method is better than other methods such as accelerated overrelaxation(AOR) and modified accelerated overrelaxation(MAOR) methods, since the spectral radius of iteration matrix in SMAOR method is less than that of the other methods. Also, we apply the method to solve a real boundary value problem.

Pfaffianized systems for a generalized Kadomtsev–Petviashvili equation

“…The Korteweg-de Vries (KdV) equation, the Boussinesq equation, the Toda lattice and the Kadomtsev-Petviashvili (KP) equation possess multi-soliton solutions and Hirota's direct method plays a crucial role in constructing soliton solutions [1][2][3]. Oriented toward the ease of use and capability of computer algebra systems, a multiple exp-function method was presented [4] to construct generic multi-exponential wave solutions, which works for more general nonlinear equations than bilinear equations [4,5]. Interestingly, some nonlinear equations even possess linear subspaces of their solutions [6].…”

A modified symmetric successive overrelaxation method for augmented systems

“…Also, Zhang and Lu [12] presented the generalized symmetric SOR (GSSOR) method for solving large sparse augmented systems. One may find details of symmetric iterative methods to solve different kinds of linear systems in [13][14][15][16][17].…”