Twelfth degree spline with application to quadrature
نویسندگان
چکیده
In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applicability and efficiency of the new method.
منابع مشابه
Time integration of rectangular membrane free vibration using spline-based differential quadrature
In this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and spline-based differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the prob...
متن کاملApplication of Higher Order Splines for Boundary Value Problems
Abstract—Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have ...
متن کاملAn Efficient Use of the Symbolic Spline-based Differential Quadrature Method in Vibration Analysis of Shells
The paper presents the differential quadrature method (DQM) based on a modified spline interpolation and the application of the method in vibration analysis of laminated, composite shells. The goal of the modification of the spline interpolation is to improve the rate of convergence and preserve the stability of the method. The modification changes the definition of the end conditions for the s...
متن کاملA Petrov–Galerkin method with quadrature for elliptic boundary value problems
We propose and analyse a fully discrete Petrov–Galerkin method with quadrature, for solving second-order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C2 splines of degree r 3, the test space consists of C0 splines of degree r − 2, and we use composite (r − 1)-point Gauss quadrature. We show existence and uniqueness of...
متن کاملGauss-Green cubature over spline curvilinear polygons
We have implemented in Matlab a Gauss-like cubature formula over bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n− 1 using N ∼ cmn nodes, 1 ≤ c ≤ p, m being the total number of points given on the boundary. It does not need any decomposition of the domain,...
متن کامل