Using Lagrange Interpolation for Numerical Solution of Two-Dimensional Fredholm Integral Equations

We present a numerical method for solving fredholm twodimensional integral equations in this study. our approach is based on two-dimensional lagrange interpolation polynomials. the use of interpolation is that instead of the unknown function, we use the lagrange interpolator polynomial, and then by solving these linear equation system, we obtain the lagrange coefficients, which are the second components of the support points, approximately. by putting these coefficients in the lagrange finder function, we get an approximation to the exact answer. a numerical algorithm is described for this purpose, and two cases are solved using this algorithm. furthermore, a theorem is proved to demonstrate the algorithm’s convergence and to obtain an upper bound on the distance between the exact and numerical solutions.