Numerical Solution of Singular Integral Equations: Methods

by Pericles S. Theocaris, Prof.; Chair of Mech. A', Athens National Technical Univ., 5 K. Zographou St., Zographou, Athens 624, Greece,

Serial Information: Journal of the Engineering Mechanics Division, 1981, Vol. 107, Issue 5, Pg. 733-752

Document Type: Journal Paper


Several methods for the numerical solution of Cauchy-type singular integral equations, frequently encountered in two-dimensional elasticity, are established. The well known numerical integration rules are properly combined in order to handle numerically Cauchy-type singular integral equations along the integration interval [-1, 1] and for a large variety of weight functions. In this way, such an equation (or a system of such equations) can be numerically sloved by reduction to a system of linear equations. For this reduction, the singular integral equation is applied to a number of appropriately selected points of the integration interval, and then a numerical integration rule is used for the approximation of the integrals in this equation.

Subject Headings: Numerical methods | Integrals | Integral equations | Approximation methods | Elastic analysis | Linear functions

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