论文信息 - A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

where the known functions h(x) , K(x, y) and g(x) are assumed to be bounded and usually to be continuous. If h(x) ~0 the equation is of first kind; if h(x) ~ 0 for a -<_ x ~ b, the equation is of second kind; if h(x) vanishes somewhere but not identically, the equation is of third kind. If the range of integration is infinite or if the kernel K(x, y) is not bounded, the equation is singular. Here we will consider only nonsingular linear integral equations of the first kind:

David L. Phillips | D. L. Phillips

[1] E. Nyström. Über Die Praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben , 1930 .

[2] P. Crout. An Application of Polynomial Approximation to the Solution of Integral Equations Arising in Physical Problems , 1940 .

[3] F. B. Hildebrand,et al. A Least Square Procedure for Solving Integral Equations by Polynomial Approximation , 1941 .

[4] G. Kreisel. Some remarks on integral equations with kernels: L (ξ1 -x1,..., ξn -xn; α) , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.