Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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29 Sep 1989TL;DR: In this paper, a spline interpolation method of subjecting given points to interpolation by using a cubic spline curve is provided, where a first-derivative vector is derived from a preset number of points including a starting point (P1), and a cubic equation between the starting point and a next point is derived based on the coordinate values of the preset points including the starting position (P 1) and the extreme point condition of the starting location (P 2 ).
Abstract: A spline interpolation method of subjecting given points to interpolation by using a cubic spline curve is provided. A first-derivative vector is derived from a preset number of points including a starting point (P1), and a cubic equation between the starting point and a next point is derived based on the coordinate values of the preset points including the starting point (P1) and the extreme point condition of the starting point (P1), to derive a spline curve between the starting point (P1) and a point (P2) next to the starting point (P1). Next, the first-derivative vector at P2 and a new next point are used instead of the starting point (P1), to derive a cubic curve between P2 and P3. In this way, a cubic equation between points is sequentially derived to obtain a cubic spline curve, and as a result, a spline curve posing no practical problems can be obtained without previously receiving all of the sequential points, while sequentially receiving the sequential points in a forward direction.
36 citations
36 citations
TL;DR: In this paper, the solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines, and the solution of the matrix equation is carried out byway of Thomas algorithm.
Abstract: Abstract The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.
36 citations
TL;DR: Embedded Diagonally Implicit Runge-Kutta methods of different orders are used for the treatment of delay differential equations and the Q-stability region of the methods is presented.
Abstract: Embedded Diagonally Implicit Runge-Kutta methods of different orders are used for the treatment of delay differential equations The delay argument is approximated using an appropriate Hermite Interpolation The numerical results based on these methods are compared and the Q-stability region of the methods are presented
35 citations
01 Jan 1988
TL;DR: Local interpolation schemes are discussed which assign tangent directions and curvatures at the data points and then join consecutive data points by parametric rational cubics, which will in general have continuous tangent direction and curvature.
Abstract: Local interpolation schemes are discussed which assign tangent directions and curvatures at the data points and then join consecutive data points by parametric rational cubics. The resulting curves possess the minimum number of inflections consistent with the data, can be modified locally by the user and will in general have continuous tangent direction and curvature. A particular scheme is suggested which will also reproduce circular arcs.
35 citations