A fast algorithm for the numerical solution of an integral equation with logarithmic kernel
The authors consider an integral equation problem. Such problems can be related to boundary value partial differential equations -- when boundary integral methods are applied, for instance. An important characteristic of the considered integral operator is that its image is not closed. This yields an ill-posed problem. However, the previous work on this topic shows that, under the suitable assumptions, one can apply a collocation-quadrature method to obtain a convergent sequence of the approximate solutions of this problem. The authors propose an algorithm which provides numerical solution of the considered problem. The main contribution of the presented work is a construction of the algorithm which reduces the complexity of the existing collocation-quadrature method while the same convergence rate is achievable. This results in accelerated algorithm. The presented numerical results show that the proposed scheme produces some significant savings of the CPU-time compared to the existing quadrature method.
scientific article; zbMATH DE number 6598875