Current Issue : January - March Volume : 2015 Issue Number : 1 Articles : 4 Articles
The conservative Helmholtz-Duffing oscillator is analyzed by means of three analytical techniques. The max-min, second-order of\nthe Hamiltonian, and the global error minimization approaches are applied to achieve natural frequencies. The obtained results\nare compared with the homotopy perturbation method and numerical solutions. The results show that second-order of the global\nerror minimization method is very accurate, so it can be widely applicable in engineering problems....
Thiswork is concernedwith the spectrumand spectral normsof r-circulant matrices with generalized k-Horadam numbers entries.\nBy using Abel transformation and some identities we obtain an explicit formula for the eigenvalues of them. In addition, a sufficient\ncondition for an r-circulant matrix to be normal is presented. Based on the results we obtain the precise value for spectral norms\nof normal r-circulant matrix with generalized k-Horadam numbers, which generalize and improve the known results....
To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial\ndifferential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion\napproach based on general basis functions (in particular case polynomial basis) for solving general operator equations, wherein the\nparticular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential\nequations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general\noperator equations in the form Lu + Nu = g(x), x ? ?, with respect to boundary condition Bu = ?, where L, N and B are\nlinear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, ? is the domain of approximation, ???? is\nan arbitrary constant, and g(x) ? L2(?) is an arbitrary function. Also the other importance of this paper is to introduce the general\nversion of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our\ndevelopment and the error analysis is presented in L2(?) norm....
The generalized regularized long wave (GRLW) equation is solved numerically by using a distributed approximating functional\n(DAF) method realized by the regularized Hermite local spectral kernel. Test problems including propagation of single solitons,\ninteraction of two and three solitons, and conservation properties of mass, energy, and momentum of the GRLW equation are\ndiscussed to test the efficiency and accuracy of the method. Furthermore, using the Maxwellian initial condition, we show that\nthe number of solitons which are generated can be approximately determined. Comparisons are made between the results of\nthe proposed method, analytical solutions, and numerical methods. It is found that the method under consideration is a viable\nalternative to existing numerical methods....
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