A weakly stable method for linear integral equations of the first kind Available to Purchase

Studies a new method of a weak approximation for a stable solution of some first kind integral equations ∫ _a^bK(x,y)u(x)dx=f(y) with continuous kernel. It is well known that the problem of resolution of these equations is ill‐posed in the sense of the methods that use the strong norms such as the one of uniform convergence. The method developed here is based on a weak formulation of the problem enabling us to weakly approach the solution and guarantee some weak stability with respect to the topology of simple convergence. An application to the inverse Laplace transform is treated at the end of this paper.