One-dimensional spline interpolation algorithms

NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

Two-dimensional spline interpolation algorithms

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

In this paper we analyze and extend mesh-free algorithms for three-dimensional data transfer problems for partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the commonrefinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a mov...

How fast can one arbitrarily and precisely scale images?

Image scaling is a frequent operation in video processing for optical metrology. In the paper, results of comparative study of computational complexity of different algorithms for scaling digital images with arbitrary scaling factors are presented and discussed. The following algorithms were compared: different types of spatial domain processing algorithms (linear, cubic, cubic spline interpola...

Adaptive Solution of One{dimensional Scalar Conservation Laws with Convex Flux

A new adaptive approach for one{dimensional scalar conservation laws with convex ux is proposed. The initial data are approximated on an adaptive grid by a problem dependent, monotone interpolation procedure in such a way, that the multivalued problem of characteristic transport can be easily and explicitly solved. The unique entropy solution is chosen by means of a selection criterion due to H...