Numerical verification method for infinite dimensional eigenvalue problems

DOI10.1007/BF03186545zbMath1184.65057MaRDI QIDQ849194

Kaori Nagatou

Publication date: 25 February 2010

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jjiam/1265033792

zbMATH Keywords

error estimatesHilbert spacedifferential operatorsinfinite dimensional eigenvalue problemnumerical verification method

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectrum, resolvent (47A10) Numerical solutions to equations with linear operators (65J10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Algorithms with automatic result verification (65G20)

Related Items (7)

Some improvements of invertibility verifications for second-order linear elliptic operators ⋮ Efficient approaches for verifying the existence and bound of inverse of linear operators in Hilbert spaces ⋮ An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces ⋮ A Numerical Verification Method for a System of FitzHugh-Nagumo Type ⋮ An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space ⋮ Some considerations of the invertibility verifications for linear elliptic operators ⋮ A computer-assisted method for excluding eigenvalues of an elliptic operator linearized at a solution of a nonlinear problem

Cites Work

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• Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method
• Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
• A numerical method to verify the elliptic eigenvalue problems including a uniqueness property
• Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators
• A computer-assisted proof on the stability of the Kolmogorov flows of incompressible viscous fluid
• Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element
• Methods for computing lower bounds to eigenvalues of self-adjoint operators
• Numerical verifications for eigenvalues of second-order elliptic operators
• NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
• A numerical approach to the proof of existence of solutions for elliptic problems II
• A numerical approach to the proof of existence of solutions for elliptic problems
• A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow
• A Procedure for Estimating Eigenvalues
• An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness
• A computer-assisted instability proof for the Orr-Sommerfeld equation with Blasius profile
• VERIFIED NUMERICAL COMPUTATIONS FOR EIGENVALUES OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• An enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems
• Computational error bounds for multiple or nearly multiple eigenvalues

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