Current Issue : October - December Volume : 2017 Issue Number : 4 Articles : 5 Articles
In this paper, we present a new sixth-order iterative method for solving nonlinear systems\nand prove a local convergence result. The new method requires solving five linear systems per\niteration. An important feature of the new method is that the LU (lower upper, also called\nLU factorization) decomposition of the Jacobian matrix is computed only once in each iteration.\nThe computational efficiency index of the new method is compared to that of some known methods.\nNumerical results are given to show that the convergence behavior of the new method is similar to the\nexisting methods. The new method can be applied to small- and medium-sized nonlinear systems....
Two numerical schemes, namely, the Taylor expansion and the variational iteration methods, have been implemented to give an\napproximate solution of the fuzzy linear Volterra integral equation of the second kind. To display the validity and applicability of the\nnumerical methods, one illustrative example with known exact solution is presented. Numerical results show that the convergence\nand accuracy of these methods were in a good agreement with the exact solution. However, according to comparison of these\nmethods, we conclude that the variational iteration method provides more accurate results....
We investigate the 3D quasilinear hyperbolic equations with nonlinear damping which describes the propagation of heat wave for\nrigid solids at very low temperature, below about 20 K. The global existence and uniqueness of strong solutions are obtained when\nthe initial data is near its equilibrium in the sense of...
The multilevel augmentation method with the anti-derivatives of the Daubechies\nwavelets is presented for solving nonlinear two-point boundary value problems. The\nanti-derivatives of the Daubechies wavelets are applied as the multilevel bases for the\nsubspaces of approximate solutions. This process results in a full nonlinear system that\ncan be solved by the multilevel augmentation method for reducing computational\ncost. The convergence rate of the present method is shown. It is the order of 2s,\n0 � s � p when p is the order of the Daubechies wavelets. Various examples of the\nDirichlet boundary conditions are shown to confirm the theoretical results....
In this article, the computation of -values known as Structured Singular\nValues SSV for the companion matrices is presented. The comparison of lower\nbounds with the well-known MATLAB routine mussv is investigated. The\nStructured Singular Values provides important tools to analyze the stability\nand instability analysis of closed loop time invariant systems in the linear\ncontrol theory as well as in structured eigenvalue perturbation theory....
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