Rigorous numerical computations for 1D advection equations with variable coefficients
DOI10.1007/s13160-019-00345-7OpenAlexW3105339397WikidataQ128434188 ScholiaQ128434188MaRDI QIDQ2318496
Yasunori Endo, Akitoshi Takayasu, Suro Yoon
Publication date: 15 August 2019
Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.02960
verified numerical computation\(C_0\) semigroupFourier-Chebyshev spectral method1D variable coefficient advection equationrigorous error bound
General methods in interval analysis (65G40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial-boundary value problems for first-order hyperbolic equations (35L04)
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Cites Work
- Numerical verification for existence of a global-in-time solution to semilinear parabolic equations
- Dissipative operators in a Banach space
- Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance
- Functional analysis, Sobolev spaces and partial differential equations
- Semigroups of linear operators and applications to partial differential equations
- Computer-assisted existence proofs for two-point boundary value problems
- Numerical verification of solutions for nonlinear hyperbolic equations
- Rigorous numerical computations for 1D advection equations with variable coefficients
- On the differentiability and the representation of one-parameter semi-group of linear operators
- Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
- Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
- Spectral Methods for Time-Dependent Problems
- A numerical approach to the proof of existence of solutions for elliptic problems
- Abstract Parabolic Evolution Equations and their Applications
- A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
- Spectral Methods in MATLAB
- A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations
- A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory
- Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation
- Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations
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