Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations |
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Institution: | Department of Information Science, Saga University, Saga 840-8502, Japan |
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Abstract: | 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. |
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