The mathematical model of some environmental physics problems is represented by a singular integral equation with an oscillatory kernel. We investigate a method for the numerical evaluation of Cauchy principal value integrals of oscillatory functions. The method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a Jacobi weight. In this way, we obtain a procedure that is numerically stable and the algorithm can be implemented in a fast way yielding satisfactory numerical results. Bounds of the error and of the amplification factor are also provided.
Numerical evaluation of the SIE solution for some environmental problems
M R Capobianco;
2001
Abstract
The mathematical model of some environmental physics problems is represented by a singular integral equation with an oscillatory kernel. We investigate a method for the numerical evaluation of Cauchy principal value integrals of oscillatory functions. The method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a Jacobi weight. In this way, we obtain a procedure that is numerically stable and the algorithm can be implemented in a fast way yielding satisfactory numerical results. Bounds of the error and of the amplification factor are also provided.File in questo prodotto:
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