On the solution of integral equations with strongly singular kernels. (English) Zbl 0631.65139
The problem of evaluating integrals having a singularity of the form \((t- x)^{-m}\), where \(m\geq 1\), is studied. Integrals with strong singularities are interpreted in the Hadamard sense and are used for obtaining approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term \((t-x)^{-m}\), terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.
Reviewer: J.Kofroň
MSC:
65R20 | Numerical methods for integral equations |
65D32 | Numerical quadrature and cubature formulas |
45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
30E20 | Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane |
74B99 | Elastic materials |
74H99 | Dynamical problems in solid mechanics |