Block Operators and Spectral Discretizations

DOI10.1137/16M1065975zbMath1365.65153MaRDI QIDQ5738137

Jared Lee Aurentz, Lloyd N. Threfethen

Publication date: 31 May 2017

Published in: SIAM Review (Search for Journal in Brave)

zbMATH Keywords

integral equationNewton iterationFredholm operatorindexODEblock matrixnonlinear problemspectral collocationchebfunblock operator

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical solutions to equations with linear operators (65J10) Numerical solutions to equations with nonlinear operators (65J15) Eigenvalue problems for integral equations (45C05) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16)

Related Items (11)

Well-conditioned ultraspherical and spectral integration methods for resolvent analysis of channel flows of Newtonian and viscoelastic fluids ⋮ Least-Squares Spectral Methods for ODE Eigenvalue Problems ⋮ Schatten-von Neumann characteristic of infinite tridiagonal block operator matrices ⋮ Spectral methods for capillary surfaces described by bounded generating curves ⋮ Eight Perspectives on the Exponentially Ill-Conditioned Equation $\varepsilon y - x y' + y = 0$ ⋮ Multi-scale spectral methods for bounded radially symmetric capillary surfaces ⋮ Model-based design of riblets for turbulent drag reduction ⋮ Polar differentiation matrices for the Laplace equation in the disk under nonhomogeneous Dirichlet, Neumann and Robin boundary conditions and the biharmonic equation under nonhomogeneous Dirichlet conditions ⋮ Resolvent-based predictions for turbulent flow over anisotropic permeable substrates ⋮ Linear stability analysis of two fluid columns of different densities and viscosities in a gravity field ⋮ Rectangular eigenvalue problems

Uses Software

• Matlab
• Chebfun

Cites Work

• Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations
• Rectangular spectral collocation
• Automatic Fréchet Differentiation for the Numerical Solution of Boundary-Value Problems
• Spectral Integration and Two-Point Boundary Value Problems
• Numerical solution of saddle point problems
• Extension of Chebfun to Periodic Functions
• Optimization with PDE Constraints
• Spectral Methods in MATLAB
• Barycentric Lagrange Interpolation
• Explicit construction of rectangular differentiation matrices
• Perspectives in Flow Control and Optimization
• An Infinite Dimensional Version of Sard's Theorem
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