Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
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 advan...
Κύριοι συγγραφείς: | , , |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Singapore :
Springer Singapore : Imprint: Springer,
2019.
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Έκδοση: | 1st ed. 2019. |
Σειρά: | Springer Series in Computational Mathematics,
53 |
Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.