Nyström method for Fredholm integral equations of the second kind in two variables on a triangle

摘要

The paper deals with the approximation of the solution of the following bivariate Fredholm integral equationf(y)-μ∫DK(x,y)f(x)ω∼(x)dx=g(y),y∈D,where the domain D is a triangle. The proposed procedure, by a suitable transformation, is essentially the Nyström method based on the zeros of univariate Jacobi orthogonal polynomials. Convergence, stability and well conditioning of the method are proved. In order to illustrate the efficiency of the proposed method some numerical tests are given.