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A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems
A numerical method to verify the invertibility of second-order linear elliptic operators by using the projection and the constructive a priori error estimates based upon the existing verification method originally developed by one of the authors is proposed.
Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
- M. Nakao, M. Plum, Y. Watanabe
- Mathematics, Computer ScienceSpringer Series in Computational Mathematics
This paper presents a new formulation for the verification of the existence of carboniferous strata, and details the methodology used, as well as some of the techniques used, in this study, to achieve this result.
A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem
AbstractA computer assisted proof of the existence of nontrivial steady-state solutions for the two-dimensional Rayleigh-Bénard convection is described. The method is based on an infinite dimensional…
A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid
- Y. Watanabe
- Mathematics, Computer Science
- 20 January 2009
Norm bound computation for inverses of linear operators in Hilbert spaces
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration
A numerical verification method for two-coupled elliptic partial differential equations
- Y. Watanabe
A numerical verification, method of steady state solutions for a system of reaction-diffusion equations is described. Using a decoupling technique, the system is reduced to a single nonlinear…
Numerical verification methods for solutions of semilinear elliptic boundary value problems
This article describes a survey on numerical verification methods for second-order semilinear elliptic boundary value problems introduced by authors and their colleagues. Here “numerical…
Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators
A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh–Bénard problems
This paper is the three dimensional extension of the two dimensional work in Nakao et al. (Reliable Comput 9(5):359–372, 2003) on a computer assisted proof of the existence of nontrivial steady state solutions for Rayleigh–Bénard convection based on the fixed point theorem using a Newton like operator.