Numerical verification methods for a system of elliptic PDEs, and their software library

摘要

Since the numerical verification method for solving boundary value problems for elliptic partial differential equations (PDEs) was first developed in 1988, many methods have been devised. In this paper, existing verification methods are reformulated using a convergence theorem for simplified Newton-like methods in the direct product space V_(h) × V _(⊥) of a computable finite-dimensional space V_(h) and its orthogonal complement space V _(⊥). Additionally, the Verified Computation for PDEs (VCP) library is provided, which is a software library written in the C++ programming language. The VCP library is introduced as a software library for numerical verification methods of solutions to PDEs. Finally, numerical examples are presented using the reformulated verification methods and VCP library.