Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

• Main Authors: Nakao, Mitsuhiro T. (Author, http://id.loc.gov/vocabulary/relators/aut), Plum, Michael (http://id.loc.gov/vocabulary/relators/aut), Watanabe, Yoshitaka (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Springer Series in Computational Mathematics, 53
• Subjects: Numerical analysis.; Computer science-Mathematics.; Computer mathematics.; Partial differential equations.; Numerical Analysis.; Mathematical Applications in Computer Science.; 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...

Table of Contents:

• 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.