Algorithm 45. Automatic computation of improper integrals over a bounded or unbounded planar region
Tóm tắt
An automatic quadrature algorithm especially designed for double integration of functions with some form of singular behaviour on the boundary of the integration region is described, and its FORTRAN code is presented. The algorithm is based on the use of the product trapezoidal rule, after a non-linear transformation of the integrand in both variables renders a new integrand function whose derivatives vanish on the (transformed) boundary. Numerical results demonstrate the ability of the algorithm to obtain high accuracies in dealing automatically with pathological singularities of non-specific types.
Tài liệu tham khảo
de Doncker, E., Piessens, R.: Algorithm 32. Automatic computation of integrals with singular integrand, over a finite or infinite range. Computing17, 265–279 (1976).
Haegemans, A.: Algorithm 34. An algorithm for the automatic integration over a triangle. Computing19, 179–187 (1977).
Iri, M., Moriguti, S., Takasawa, Y.: On a numerical integration formula. Kolyuroku Research Institute for Mathematical Sciences, Kyoto University, Nr. 91,1970, 82. (In Japanese.)
Lyness, J. N., Kaganove, J. J.: Comments on the nature of automatic quadrature routines. Comp. J.20, 170–177 (1977).
Takahasi, H., Mori, M.: Error estimation in the numerical integration of analytic functions. Report of the Computer Centre (University of Tokyo)3, 41–108 (1970).
van Dooren, P., de Ridder, L.: Algorithm 6. An adaptive algorithm for numerical integration over ann-dimensional cube. J. of Comp. and Appl. Math.2, 207–217 (1976).