ASYMPTOTIC ESTIMATION OF GAUSSIAN QUADRATURE ERROR FOR A NONSINGULAR INTEGRAL IN POTENTIAL THEORY

Abstract. This paper considers the n-point Gauss-Jacobi approximation of nonsingular integrals of the form ∫ 1 µ(t)φ(t)log(z−t)dt, with Jacobi weight −1 µ and polynomial φ, and derives an estimate for the quadrature error that is asymptotic as n → ∞. The approach follows that previously described by Donaldson and Elliott. A numerical example illustrating the accuracy of the asymptotic estimate is presented. The extension of the theory to similar integrals defined on more general analytic arcs is outlined. 1

ASYMPTOTIC ESTIMATION OF GAUSSIAN QUADRATURE ERROR FOR A NONSINGULAR INTEGRAL IN POTENTIAL THEORY

Abstract. This paper considers the n-point Gauss-Jacobi approximation of nonsingular integrals of the form � 1 µ(t)φ(t)log(z−t)dt, with Jacobi weight −1 µ and polynomial φ, and derives an estimate for the quadrature error that is asymptotic as n → ∞. The approach follows that previously described by Donaldson and Elliott. A numerical example illustrating the accuracy of the asymptotic estimate is presented. The extension of the theory to similar integrals defined on more general analytic arcs is outlined. 1