Titlebook: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations; Mitsuhiro T. Nakao,Michael Plum,Yoshitaka

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

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Infinite-Dimensional Newton-Type Methodpplying the same principle as in Chaps. 1 and 2. After that, we confirm the existence of solutions by proving the contractility of the infinite-dimensional Newton-like operator with a residual form. Note that a projection into a finite-dimensional subspace and constructive error estimates of the projection play important and essential roles.

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Basic Principle of the Verificationl improvements have since been made. This method consists of a projection and error estimations by the effective use of the compactness property of the relevant operator, and it can be represented in a rather generalized form in the examples below.

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Other Problem Typesf second-order elliptic boundary value problems, where the linearized operator . lacks symmetry, whence a norm bound for .. cannot be computed via the spectrum of . or ....In this chapter we concentrate on the main ideas and partially will be a bit less extensive with technical details.

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Eigenvalue Bounds for Self-Adjoint Eigenvalue Problemssical application is quantum physics, but also other fields like electro-dynamics (including optics) or statistical mechanics are governed by partial differential operators and related eigenvalue problems.

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