We propose a numerical verification method which proves the existence of solutions to two-point boundary value problems and leads their guaranteed error estimates for approximate solutions by finite element method. The ‘guaranteed’ error bound is ...
We propose a numerical verification method which proves the existence of solutions to two-point boundary value problems and leads their guaranteed error estimates for approximate solutions by finite element method. The ‘guaranteed’ error bound is rigorous, i.e. it takes every error such as the discretization error and the rounding error when solving the problems into account. We define an approximate solution operator for a linearized problem by some matrix form. The fixed-point formulation is led by operator equations. By using Banach’s fixed-point theorem, the existence of solution and guaranteed error bounds can be obtained. Finally, numerical example is presented.