Application of Splines of the Fifth Order Approximation for Solving Integral Equations of the Second Kind with a Weak Singularity

Previously, the authors showed that local splines of the different order of approximation give good results on both uniform and non-uniform grids. In this paper, we investigate the stability of the numerical method based on the splines of the fifth order of approximation and the use of these splines for solving weak singular Fredholm and Volterra integral equations of the second kind. The solution method consists of replacing the unknown function under the integral sign with a spline approximation. We compare the errors of the solutions of integral equations obtained using splines of the second, fifth, and seventh orders with the results which were received in recent papers by using other methods. The results of the numerical experiments are presented in this paper.