Explicit Gaussian quadrature rules for C1 cubic splines with symmetrically stretched knot sequences

R. Ait-Haddou, M. Barton, V.M. Calo
Journal of Computational and Applied Mathematics, volume 290, 543-552, (2015)

Explicit Gaussian quadrature rules for C1 cubic splines with symmetrically stretched knot sequences

Keywords

Gaussian quadrature, Cubic splines, Peano kernel, B-splines

Abstract

​We provide explicit expressions for quadrature rules on the space of C1C1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.

Code

DOI: 10.1016/j.cam.2015.06.008

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