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Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: In this article, an improved homogeneous balance principle and an F-expansion technique are used to construct exact self-similar solutions to the cubic-quintic nonlinear Schrodinger equation.
Abstract: An improved homogeneous balance principle and an F-expansion technique are used to construct exact self-similar solutions to the cubic-quintic nonlinear Schrodinger equation. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and the external potential. Some simple self-similar waves are presented.
14 citations
TL;DR: In this paper, the generalized quintic complex Ginzburg-Landau equation is considered to be solved by means of the homotopy analysis method (HAM), by plotting the h-curve of the examples, the region of convergence is determined.
14 citations
TL;DR: An accurate and efficient algorithm for obtaining all roots of general real cubic and quartic polynomials and shows that a stable Newton-Raphson iteration on a derived symmetric sixth degree polynomial can be formulated for the real parts of the complex roots.
Abstract: We report on an accurate and efficient algorithm for obtaining all roots of general real cubic and quartic polynomials. Both the cubic and quartic solvers give highly accurate roots and place no restrictions on the magnitude of the polynomial coefficients. The key to the algorithm is a proper rescaling of both polynomials. This puts upper bounds on the magnitude of the roots and is very useful in stabilizing the root finding process. The cubic solver is based on dividing the cubic polynomial into six classes. By analyzing the root surface for each class, a fast convergent Newton-Raphson starting point for a real root is obtained at a cost no higher than three additions and four multiplications. The quartic solver uses the cubic solver in getting information about stationary points and, when the quartic has real roots, stable Newton-Raphson iterations give one of the extreme real roots. The remaining roots follow by composite deflation to a cubic. If the quartic has only complex roots, the present article shows that a stable Newton-Raphson iteration on a derived symmetric sixth degree polynomial can be formulated for the real parts of the complex roots. The imaginary parts follow by solving suitable quadratics.
14 citations
TL;DR: In this paper, the authors considered the G interpolation by Pythagorean-hodograph (PH) quintic curves in R, d ≥ 2, and obtained results turn out as a useful tool in practical applications.
Abstract: In this paper, the G interpolation by Pythagorean-hodograph (PH) quintic curves in R, d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method. AMS subject classifications: 65D05, 65D17
14 citations
TL;DR: In this article, the application of cubic B 3 spline, quintic B 5 spline functions and eigenfunctions which satisfy the boundary conditions to obtaining the approximate solution for the static analysis of a flat cylindrical shell is discussed.
14 citations