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

• Rachid Ait-Haddou ^[1] ; Michael Bartoň ^[1] ; Victor Manuel Calo ^[1]
  1. [1] King Abdullah University of Science and Technology

     King Abdullah University of Science and Technology

     Arabia Saudí

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 543-552
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.06.008
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• Resumen

  • We provide explicit expressions for quadrature rules on the space of C1 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.