a b s t r a c tIn this paper, we establish a modified symmetric successive overrelaxation (MSSOR) method, to solve augmented systems of linear equations, which uses two relaxation parameters. This method is an extension of the symmetric SOR (SSOR) iterative method. The convergence of the MSSOR method for augmented systems is studied. Numerical examples show that the new method is an efficient method.
SUMMARYIn this paper, we present three kinds of preconditioners for preconditioned modified accelerated overrelaxation (PMAOR) method to solve systems of linear equations. We show that the spectral radius of iteration matrix for the PMAOR method is smaller than that for modified accelerated over-relaxation (MAOR) method including their comparison. The comparison results show that the convergence rate of the PMAOR method is better than the rate of the MAOR method. We provide some numerical results for the evidence of our method. Also we compare our numerical results with solutions by variational iteration method.
The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface. The spectral element collocation method is then employed to complex geometries; that is, we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain. We give some numerical experiments to show efficiency of our algorithm and its spectral convergence.
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