Approximating solutions of fredholm integral equations via a general spline maximum entropy method

In this paper, we describe a general spline maximum entropy method for the approximation of solutions for solving Fredholm integral equations. The general spline maximum entropy method allows to extract piecewise linear, piecewise quadratic, piecewise cubic, piecewise quartic, piecewise quintic and other maximum entropy methods for solving Fredholm integral equations. We present numerical examples of piecewise linear, piecewise quadratic, piecewise cubic, piecewise quartic, piecewise quintic and other piecewise maximum entropy methods for solving Fredholm integral equations of second kind and first kind respectively. A proof of convergence for the piecewise spline maximum entropy method is also presented.