Piecewise Linear Maximum Entropy Method for Fredholm Integral Equations with Weakly Singular Kernel

Approximate solution of Fredholm integral equations with certain types of weakly singular algebraic kernels is obtained by the piecewise linear maximum entropy method. During implementation of the method, two-dimension numerical integration is reduced to one-dimension numerical integration, which allows to lower the computational cost. The results of numerical experiments are consistent with theoretical findings and show the effectiveness of the method.