Numerical Solution of Integral Equations Using Legendre Polynomials

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Abstract
This paper deals with the solution of certain integral equations of displacement type. A previously developed theory, which uses an expansion of the solution in Legendre polynomials, is applied to two special cases. One is a singular equation encountered in polymer physics. The results of the Legendre expansion are compared with calculations based on two other recently proposed methods, and the merits of an expansion in Gegenbauer polynomials are discussed. For the second case, which arises in electrodynamics, a very accurate solution is given for a large range of parameter values.

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