American Society of Civil Engineers

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)

Journal of the Engineering Mechanics Division
, Vol. 107, No. 5, September/October 1981, pp. 733-752

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Document type: Journal Paper
Abstract: 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.

ASCE Subject Headings:
Numerical analysis
Integral equations