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Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations

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概要 We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a $ 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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登録日 2009.04.22
更新日 2017.01.20