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We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a $ C^1 $ finite element solution and an ine...quality 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 $ L^p $ -space in a computer. We present detailed verification procedures and give some numerical examples.続きを見る
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