No abstract

No abstract

No abstract

An adaptive algorlthm for computing an approximation to the integral of each element in a vector function N x, y) over a two-dimensional region made UP of triangles is presented. A FORTRAN implementation of the algorithm is included. The basic cubature rule used over each triangle is a 37-point symmetric rule of degree 13. Based on the same evaluation points the local error for each element in the approximation vector and for each triangle is computed using a sequence of null rule evaluations. A sophisticated error-estimation procedure tries, in a cautious manner, to decide whether we have asymptotic behavior locally for each function. Different actions are taken depending on that decision, and the procedure takes advantage of the basic rule's polynomial degree when computing the error estimate in the asymptotic case.

A new algorithm for estimating the error in quadrature approximations is presented. Based on the same integrand evaluations that we need for approximating the integral, one may, for many quadrature rules, compute a sequence of null rule approximations. These null rule approximations are then used to produce an estimate of the local error. The algorithm allows us to take advantage of the degree of precision of the basic quadrature rule. In the experiments we show that the algorithm works satisfactorily for a selection of different quadrature rules on all test families of integrals.