This paper provides a method of solution for functional, differential, and integral equations. The method is based on Schauder’s and Darbo’s fixed point theorems on computation of bounds and existence/uniqueness verification of the solution of a fixed point equation set in function space (see ).
By means of the developments presented in this paper, close and reliable bounds are effectively computed with the solution error automatically controlled. To show the applications of the metod, the author provides seven examples dealing with:
evaluation of an elliptic integral,
solution of several boundary value problems.
evaluation of transcendental integrals, and
evaluation of double integrals.
The paper should be of particular interest to software developers in the areas of functional, differential, and integral equations.