A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian #ux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme is strictly mass conservative and positive de"nite while maintaining high peak retention. The new algorithm is compared ...

The regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method. The same method is applied to the time-split RLW equation. Comparison is made with both analytical solutions and some previous results. Propagation of solitary waves, interaction of two solitons are studied. © 2005 Elsevier B.V. All rights reserved. MSC: 65N30; 65D07; 76B25

In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates the solutions, and their higher order derivatives of differential equations. Numerical illustrations are tabulated to demonstrate the practical usefulness of ...

The basic idea of the Meir/Sharma/Hall/Meyer error analysis for cubic spline interpolation (see [SM66], [H68], [HM76]) has been extended to cover also certain deficient quartic and quintic spline interpolation schemes, the latter already by them, the former by Howell/Varma [HV89] and, perhaps, others. It is the purpose of this note to describe the most general situation to which this idea appli...

The algorithms and programs in this handy book deal almost exclusively with cubic splines. A short introduction stresses the maximum "smoothness" of "natural" splines. The next chapter reviews the numerical solution of tridiagonal linear systems by Gauss elimination and of block tridiagonal linear systems by relaxation. Chapter 3 offers programs for cubic spline interpolation with various (sepa...

This paper presents a new motion planning primitive to be used for the iterative steering of vision-based autonomous vehicles. This primitive is a parameterized quintic spline, denoted as -spline, that allows interpolating an arbitrary sequence of points with overall second-order geometric ( -) continuity. Issues such as completeness, minimality, regularity, symmetry, and flexibility of these -...

B-spline scaling functions and wavelets have found wide applicability in many scientific and practical problems thanks to their unique properties. They show considerably better results in comparison to other wavelets, and they are used as well in mathematical approximations, signal processing, image compression, etc. But only the first four wavelets from this family were mathematically formulat...

Spline quasi-interpolants are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline quasi-interpolants on uniform partitions of the real line having small infinite norms. We call them near minimally normed quasi-interpolants: they are exact on polynomial spaces and minimize a simple upper bound of their infinite norms. We give...

For many design applications, where multiple primary surface pieces meet, the distribution of curvature is more important than formally achieving exact curvature continuity. For parametric spline surfaces, when constructing a multi-sided surface cap, we demonstrate a strong link between the uniform variation of the re-parameterization between (boundary) data of the joining pieces and a desirabl...