doi:10.3850/978-981-08-5118-7_054

ABSTRACT

A guaranteed error estimate procedure for linear or nonlinear two-point boundary value problems is established by authors. ‘Guaranteed’ error estimate is rigorous, i.e. it takes into account every error such as the discretization error and the rounding error when we compute an approximate solution. We can also prove the existence and the uniqueness of the exact solution. Namely, we can solve the problem with mathematically rigorous. In order to bound the guaranteed error, an inverse operator norm estimation is needed. In the previous work of authors, the inverse operator estimate needs the norm of the inverse matrix, which is a posteriori constant. So we need much time to compute the inverse operator norm estimation. In this paper, we propose a priori estimation concerning the inverse operator. The proposed estimate is given without the norm of the inverse matrix. By using a priori estimation, we can estimate the inverse operator as a priori constant. An extremely improvement of the computational speed is expected. On the other hand, it needs a condition to use a priori estimation. Finally, we present some numerical results.

Keywords: A priori estimates, Guaranteed error estimate, Numerical verification.

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