Numerical Solution of Singular Integral Equations Arising in Mixed Boundary Value Problems of Elasticity.
Final rept. 1 Nov 79-30 Jun 83.
STATE UNIV OF NEW YORK AT STONY BROOK
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The central theme of this project was the development and analysis of direct methods, based on collocation for the solution of singular integral equations with a principal value integral. These equations arise in such diverse fields as linear elastic fracture mechanics, neutron transport, long water waves, image reconstruction and radiative transfer. In the classical approach, the singular integral equation is regularized to yield a Fredholm integral equation of the second kind. The numerical implementation of the regularization is usually quite cumbersome. While direct methods proposed by Erdogan. Erdogan and Gupta, and Theocaris and Ioakimidis have been used in Fracture Mechanics, their convergence and stability has received scant attention. The work at Stony Brook has made important strides in both directions. The author analyzed the behavior of approximate solutions enhancing our understanding of the convergence and stability of the methods based on Gaussian quadrature. He has also proposed methods which can be employed in the situations where the Gaussian quadrature-collocation schemes fail. Author
- Numerical Mathematics