Rigorous computation of Nekrasov’s integral equation for water waves

Nekrasov’s integral equation is a mathematical model for two-dimensional, periodic, symmetric and progressive waves on the surface of water. Although some iterative numerical methods have been developed for this type of integral equation, high dimensional approximation is required for the case of large wave height. This paper proposes the method of error estimate for this problem using a numerical verification technique based on a fixed point theorem and interval analysis. This method enables us to show existence of exact solutions in a neighborhood of an approximate solution.