Numerical Existence and Uniqueness Proof for Solutions of Nonlinear Hyperbolic Equations Numerical Existence and Uniqueness Proof for Solutions of Nonlinear Hyperbolic Equations
نویسنده
چکیده
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 nite 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 xed point theorem for a continuous map on L p -space in a computer. We present detailed veri cation procedures and give some numerical examples.
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