The reduction method for approximative solution of systems of Singular Integro-Differential Equations in Lebesgue spaces (case γ ≠ 0)

摘要

In this article we have elaborated the numerical schemes of reduction methods for approximate solution of system of singular integro-differential equations when the kernel has a weak singularity. The equations are defined on the arbitrary smooth closed contour of complex plane. We suggest the numerical schemes of the reduction method over the system of Faber-Laurent polynomials for the approximate solution of weakly singular integro-differential equations defined on smooth closed contours in the complex plane. We use the cut-off technique kernel to reduce the weakly singular integro-differential equation to the continuous one. Our approach is based on the Krykunov theory and Zolotarevski results. We have obtained the theoretical background for these methods in classical Lebesgue spaces.