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Explicit Error Estimation for Boundary Value Problems

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Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

This chapter presents recent advancements in quantitative error estimates, specifically providing concrete error bounds for boundary value problems in partial differential equations. These error estimates are crucial for obtaining explicit eigenvalue bounds. A primary focus is on the a priori error estimation based on the hypercircle method (i.e., the Prager–Synge theorem), offering a novel approach for projection error estimation in the analysis of eigenvalue problems.

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Authors and Affiliations

  1. Tokyo Woman’s Christian University, Suginami-ku, Tokyo, 167-8585, Japan

    Xuefeng Liu

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  1. Xuefeng Liu
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Liu, X. (2024). Explicit Error Estimation for Boundary Value Problems. In: Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems. SpringerBriefs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-97-3577-8_2

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