Abstract
One of the authors have proposed a method to prove the existence and the local uniqueness of solutions to infinite-dimensional fixed-point equations using computer. However, for second-order elliptic boundary value problems, in the case the equation includes the first-order term, it turned out that there is a possibility that the verification algorithm come to an end unsuccessfully. The purpose of this paper is to propose an alternative method to overcome this difficulity. Numerical examples compared with the previous algorithm confirm the effectiveness of the new method.
