Showing papers on "Quintic function published in 1990"
TL;DR: In this paper, the authors formulate semi-direct MP2 methods that utilize disk space (which is usually much larger than memory size) for the steps that require most storage, and show that these methods are superior to conventional algorithms despite requiring less disk space.
1,189 citations
TL;DR: In this paper, a class of variational inequalities related with contact problems in elastostatics can be characterized by a sequence of Variational equations, which are solved using modified quintic splines collocation methods.
36 citations
TL;DR: An algorithm which determines a bivariate smooth piecewise polynomial interpolant to function values given at points scattered in R 2fs so that the degree of the polynomials will be as small as possible for arbitrary triangulations and a high degree ofPolynomial precision is achieved.
15 citations
TL;DR: The innovative part of the algorithm is the formulation of a bivariate nonic Hermite polynomial with C2-property contained in modules CBSIDE, CSINSD, and CSHORN, which describes a twice differentiable polynometric representation on a set of triangles.
Abstract: The innovative part of the algorithm is the formulation of a bivariate nonic Hermite polynomial with C2-property [7] contained in modules CBSIDE, CSINSD, and CSHORN. These formulas are of principal value. They describe a twice differentiable polynomial representation on a set of triangles. To be of immediate use, some interfaces were designed, and the new modules were integrated into Renka’s triangle interpolation package [9]. Especially all procedures related to the generation and the handling of triangles are taken or may be taken from that algorithm. Also, the method of derivative estimation is identical with Renka’s global method [S]. The higher derivatives of order n are generated by taking the derivatives of order n 1 as input (n = 2, 3, 4). For the sake of completeness, equivalent routines for Cl-interpolation (once differentiable) are supplied, based on the well known quintic triangular element [l, 3, 41. In general, the Cl-routines are approximately 3 times faster than their C ‘-equivalents and need less memory. The main user interfaces to the package are the routines C2GRID and ClGRID. They interpolate values of a rectangular grid to a given set of irregularly distributed points (scattered data interpolation in two dimensions). Because the array of grid points is scanned for every triangie, the coefficients for each polynomial are computed only once, and the fast evaluation phase of the Taylor representation [7] can be exploited most efficiently. If the mesh lines of the rectangular grid are relatively wide with respect to the irregularly distributed
13 citations
TL;DR: In this article, a unified method for solving algebracially quadratic, cubic and quartic equations is presented, which leads to a simple, complete system of the four solutions to the general quartic equation.
Abstract: It seems in the literature that methods for solving algebracially quadratic, cubic and quartic equations have very little in common. The goal of this article is to present a unified method for obtaining the algebraic solution of these equations. It is interesting to realize that the unified method presented here leads to a simple, complete system of the four solutions to the general quartic equation. The simplicity of this system of solutions makes it worthwhile to revisit some old problems related to cubic and quartic equations
12 citations
TL;DR: In this article, a class of variational inequalities related with contact problems in elastostatics can be characterized by a sequence variational equations, which are solved by using the modified quintic splines collocations method.
9 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: In this article, the authors adopt cubic and quintic polynomial shape functions in the lower-order and higher-order analysis, respectively, based upon the principle of minimum potential energy.
8 citations
TL;DR: In this paper, the authors considered a class of forced delay differential equations in which the delay is given by π/2 and investigated the problem of finding its special periodic solutions.
Abstract: We consider a class of forced delay differential equations in which the delay is given by π/2 and investigate the problem of finding its special periodic solutions. We first approximate these by a Rayleigh-Ritz-Galerkin sequence. Our second method introduces an averaged model thought to give a qualitative approximation to the solution behavior. The effects of cubic and quintic nonlinearities are compared.
01 Jan 1990
TL;DR: In this article, the method of symmetry reduction for nonlinear partial differential equations and its combination with singularity analysis is reviewed and physical examples such as the quintic multidimensional Schrodinger equation are discussed.
Abstract: The method of symmetry reduction for nonlinear partial differential equations and its combination with singularity analysis is reviewed. Physical examples, such as the quintic multidimensional Schrodinger equation, are discussed.