ON SOME GAUSS AND LOBATTO BASED INTEGRATION FORMULAE,
QUEEN'S UNIV BELFAST (NORTHERN IRELAND) DEPT OF APPLIED MATHEMATICS
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The economy of the Gaussian quadrature formulae for carrying out numerical integration is to some extent reduced by the fact that an increase in the order of the formulae makes no use of previous integrand evaluations. In the paper a set of integration formulae is derived based on a set of 2 to the r power 1 Gauss or Lobatto points, where r is an integer. In carrying out an integration the number of points is successively increased until convergence appears satisfactory or until the number of points reaches 2 to the r power 1 corresponding to the full Gauss or Lobatto formula. Since each subset includes the points of the previous subset no integrand evaluations are wasted.
- Numerical Mathematics