Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations

摘要

We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a C1 finite element solution and an inequality constituting a bound on the norm of the inverse operator of the linearized operator, we numerically construct a set of functions which satisfy the hypothesis of Banach's fixed point theorem for a continuous map on Lp-space in a computer. We present detailed verification procedures and give some numerical examples.