On the numerical solution of integral-equations

Abstract

The present communication is concerned with integral-equations of Abel’s type ∫ 0 x ϕ (s) k (x - s) ds = f(x) , (1) and of Poisson’s type ϕ (x) + ∫ 0 x ϕ (s) k (x - s) ds = f(x) , (2) where k (x) is a given function called the nucleus , f(x) is also a given function, and ϕ(x) is the unknown function which is to be determined. The object of the work is to obtain solutions of these equations in forms which can be made the basis of numerical calculation.