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Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
ISBN-13:
9789811376696
Veröffentl:
2019
Seiten:
467
Autor:
Mitsuhiro T. Nakao
Serie:
53, Springer Series in Computational Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a "theoretical" proof) of additionally providing accurate quantitative information.
1. Basic principle of the verification.- 2. Newton-type approaches in finite dimension.- 3. Infinite dimensional Newton-type method.- 4. Applications to the computer-assisted proof in analysis.- 5. Evolutional equations.- 6. Eigenvalue enclosures for selfadjoint operators.- 7. Abstract formulation F(u) = 0, and the basic theorem.- 8. Strong solutions for second-order problems.- 9. Weak solutions for second-order problems.- 10. Weak solutions for fourth-order problems.- 11. Parameter-dependent problems.- 12. Non-selfadjoint eigenvalue problems.- 13. Some other methods.
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