SUMMARYWhen solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition.
Abstract. In this paper, we propose an accelerating scheme of convergence of numerical solutions of fuzzy non-linear equations. Numerical experiments show that the new method has significant acceleration of convergence of solutions of fuzzy nonlinear equation. Three-dimensional graphical representation of fuzzy solutions is also provided as a reference of visual convergence of the solution sequence.
In this paper, a non-overlapping second-order domain decomposition method for solving three-dimensional hyperbolic partial differential equation is proposed. Unconditional stability of the algorithm is analyzed. Numerical experiments show that the method is stable and very efficient.
Mathematics Subject Classification: 65M06, 65M55
In this paper, an efficient numerical method to solve fuzzy non-linear equations is proposed. It is an extension of the bi-section method, however, total number of iterations of the new method is less than the bi-section method. Numerical experiment supports its fast convergence.
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