Improvement of Numerical Verification Results of Semilinear Elliptic Boundary Value Problems

Abstract

Abstract. We improve numerical verification results of semilinear elliptic problems through the verification of a certain linear problem. As a feature of the method described in this paper, the norm of the correction term of Newton’s method, which was conventionally evaluated by the product of an inverse-operator norm and the residual norm, is more precisely evaluated through numerical verification for the linear problem derived from an original problem. This not only improves error estimations of many approximate solutions but also enables us to verify low precision approximate solutions whose error bounds could not be evaluated.