Showing papers on "Quintic function published in 1980"
TL;DR: A new fourth order method using quintic polynomials for the smooth approximation of the two point boundary value problems involving second order differential equations lacking the first derivative, which outperforms the well-known fourth order Noumerov's finite difference scheme.
Abstract: A new fourth order method using quintic polynomials is designed in this paper for the smooth approximation of the two point boundary value problems involving second order differential equations lacking the first derivative. The present method enables us to approximate the unknown function as well as its derivative at every point of the range of integration and thus it has obvious advantages over other discrete numerical methods. Our present method outperforms the well-known fourth order Noumerov's finite difference scheme. The convergence of the method is briefly outlined using matrix algebra and two numerical illustrations are provided to demonstrate the practical suitability of our approach.
46 citations
TL;DR: In this article, necessary formulas for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems were developed, which enable approximate the solution of the boundary value problem, as well as their successive derivatives smoothly.
Abstract: Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four techniques.
15 citations
TL;DR: In this paper, a new class of C 2 piecewise quintic interpolatory polynomials is defined, which contains a number of interpolatory functions which present practical advantages, when compared with the conventional cubic spline.
Abstract: A new class of C 2 piecewise quintic interpolatory polynomials is defined. It is shown that this new class contains a number of interpolatory functions which present practical advantages, when compared with the conventional cubic spline.
2 citations
TL;DR: In this paper, a curved finite element for the solution of shells of revolution is presented, where the shell geometry in general is approximated by a third order interpolation function with cubic and quintic polynomials.
Abstract: In this paper a curved finite element for the solution of shells of revolution is presented. The shell geometry in general, is approximated by a third order interpolation function. The displacement field has four components—three displacements and the rotation of the meridional plane of the of the shell. The displacement field is interpolated with cubic and quintic polynomials. The linear system involving the nodal unknowns is obtained from the principle of virtual work, together with the colateral condition relating the rotation to the other components of the displacement field. It is shown that broken generating lines for the shell surface do not limit the convergence of the solution. Finally, for numerical applications for static and dynamical problems presented.
1 citations
01 Jan 1980
TL;DR: In this article, necessary formulas for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems were developed, which enable the solution of the boundary value problem, as well as their successive derivatives smoothly.
Abstract: Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four