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 article, the nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution.
Abstract: The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period as well as the exact analytic solution is given in terms of the famous Weierstrass elliptic function. An integrable case of a damped cubic-quintic equation is presented. Mathematica code for solving both cubic and cubic-quintic Duffing equations is given in Appendix at the end.
8 citations
8 citations
TL;DR: In a footnote to a short early paper (1844) G. Eisenstein gave an analytic solution of the general quintic equation as mentioned in this paper, and discussed this remark in relation to the well-known work of Hermite (1858) and Kronecker (1861).
8 citations
TL;DR: A general theory about the existence and the uniqueness of the optimal approximant is presented and a rigorous analysis is done for some special cases for which the degree of the polynomial curve and the order of the geometric smoothness differ by two.
8 citations
TL;DR: A numerical scheme for the singular Emden–Fowler problem using quintic B-spline is investigated and the singularity of the problem is eliminated according to Lopita's law and a new high-precision solution is obtained through a linear combination of the original solutions.
Abstract: In this paper, we investigate a numerical scheme for the singular Emden–Fowler problem using quintic B-spline. We eliminate the singularity of the problem according to Lopita's law and obtain a new...
8 citations