Analytic-numerical solution with a priori error bounds for lateral vibrations of a string with variable tension and mass density

Abstract

In this paper a constructive method for computing analytic-numerical solutions with a priori error bounds for lateral vibrations of a string with variable tension and mass density is proposed. First, an exact series solution is obtained. Given an admissible error ∈ and a bounded subdomain D, an analytic numerical approximation is constructed so that the error with respect to the exact solution is less than ∈ uniformly on D.