A Method for Solving the Fredholm Integral Equation of the First Kind

The paper considers a numerical method for solving the Fredholm integral equation of first kind. essence is to replace original with corresponding regularized second kind, which then solved by modified spline collocation method. solution in this case represented as linear combination minimal splines. coefficients at splines are computed using local approximation (in some cases, quasi-interpolation) methods. Results experiments presented and show that on model problems, proposed yields sufficiently accurate approximations, accuracy can be improved nonpolynomial related functionals.