Some versions of the subdomain method for integral equations of the first kind (Q677787)

The author deals with the subdomain method to solve the integral equation \[ \int_0^1 K(t,s)x(s)ds= y(t),\qquad 0\leq t\leq 1, \] where the kernel has the form \(K(t,s)= L(t,s)\) for \(s\leq t\), and \(K(t,s)= M(t,s)\) for \(s>t\), with smooth functions \(L\), \(M\), and \(y\). The solution and its approximations admit Dirac delta-functions \(\delta(t)\), \(\delta(1-t)\) and their derivatives.