Topic
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 paper, it was shown that a single cubic segment can be used as a transition curve with the guarantee that an S-shaped transition curve will have no curvature extrema, and a C-shaped contour will have a single curvature extremum.
34 citations
TL;DR: A quintic non-polynomial spline functions is used to develop a numerical method for computing approximations to the solution of a system of fourth-order boundary-value problems associated with plate deflection theory.
34 citations
TL;DR: This paper reduces the problem of solving index form equations in quartic number fields K to the resolution of a cubic equation F ( u, v ) = i and a corresponding system of quadratic equations Q 1, Q 2 = v, which enables a fast algorithm for calculating "small" solutions of index form equation in any Quartic number field.
34 citations
TL;DR: In this article, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrodinger (NLS) equation.
Abstract: In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrodinger (NLS) equation. For this purpose, first of all, the Schrodinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, $L_{2}$
and $L_{\infty}$
, as well as the two lowest invariants, $I_{1}$
and $I_{2}$
, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.
34 citations
TL;DR: In this paper, a geometric interpretation of the solution of the General Quartic Polynomial is presented, and the solution can be interpreted as a solution of a solution to a set of problems.
Abstract: (1996). A Geometric Interpretation of the Solution of the General Quartic Polynomial. The American Mathematical Monthly: Vol. 103, No. 1, pp. 51-57.
34 citations