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

This book is the first publication in the world as a monograph on the concerned research fieldNakao and Plum are pioneers of the numerical verification method of solution for PDEs
This book offers the basic principle of verification techniques for PDEs as well as interested applications for computer assisted proofs of nonlinear problems

Is the first published monograph on computer-assisted proofs Presents pioneering work on the numerical verification method of solution for partial differential equations Provides verification techniques for partial differential equations and applications for computer-assisted proofs

Résumé

"Each chapter of the book is written in an excellent, easy-to-understand way, both in terms of items, proofs, and codes. The reader himself can easily check the simplicity and correctness of the codes." (Rózsa Horváth-Bokor, zbMATH 1462.65004, 2021)

Contenu

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.