Cubic Spline Solution of Integral Equations.

摘要

The solution of linear integral equations of the form f1(x)g(x)+f2(x)g(x)+f3(x) = integral from a(x) to b(x) of k(x,y)g(p(x,y))dy is considered. The equations are reduced to a set of linear algebraic equations in the values of g(x) on a finite mesh. The method entails formal orthogonal polynominal quadrature of the integral and subsequent formal cubic spline interpolation for the values of g at the mesh points. Discontinuities in the derivatives of g are accommodated. (Author)