Spline collocation for strongly elliptic equations on the torus.
The equations of physics are mathematical models consisting of geometric objects and relationships between then. There are many methods to discretize equations, but few maintain the physical nature of objects that constitute them. To respect the geometrical nature elements of physics, it is necessary to change the point of view and using differential geometry, including the numerical study. We propose to construct discrete differential forms using B-splines and a formulation discrete for different...
AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...