Spectral Methods in MATLAB

By Lloyd N. Trefethen. 2000

4,468 citations recorded by the source corpus.

Subfields: Computational Mechanics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/d343e37da5fcb61db8c65e8ba3bb91a98f1befe5

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In Computational Mechanics

In Environmental Engineering

Citations in the corpus

Solving PDEs with radial basis functions * (2015, methodology): “That limit provides an alternative way to understand and use pseudospectral (PS) methods (Boyd 2000, Fornberg 1996, Trefethen 2000).”
Spectral Algorithm for Pseudospectral Methods in Optimal Control (2008, methodology): “Several variants of a spectral algorithm can be designed based on the collection of theoretical results presented in Sec.”
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, background): “A good choice for these nodes is the well-known Gauss and Gauss–Lobatto points [20,30], where lie inside [0,T] and are clustered near the endpoints.”
Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, methodology): “[45] L.”
Continuation and Bifurcation Analysis of Delay Differential Equations (2007, neutral): “There are several different spectral collocation methods for partial differential equations that could be used to solve (32); for an introduction see Trefethen [76].”
A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations (2015, methodology): “Spectral methods (see, for instance [1–6]) are one of the principal methods of discretization for the numerical solution of differential equations.”
Monarch: Expressive Structured Matrices for Efficient and Accurate Training (2022, background): “Another class of structured matrices, such as Fourier, sine/cosine, Chebyshev, are used in specialized domains such as PDE solving (Trefethen, 2000) and medical imaging (Hsieh, 2003).”
An improved Levin quadrature method for highly oscillatory integrals (2010, methodology): “The Chebyshev differentiation matrix [1,2,5,22,24], which is a powerful tool in the Chebyshev pseudo-spectral method, is employed to solve the ODE (2).”
Using meshfree approximation for multi-asset American option problems (2004, methodology): “Since our radial basis functions do not satisfy the boundary conditions automatically, they are satisfied by adding specific equations to enforce them at each time step just as in traditional spectral methods (see, e.g., [ 21 ], and step 6(e) in the algorithm below).”
Legendre Pseudospectral Approximations of Optimal Control Problems (2003, background): “In this sense, they most closely resemble finite element methods but offer a far more impressive convergence rate known as spectral accuracy[ 17 ].”
Barycentric Lagrange Interpolation (2004, background): “Some French and German authors have described the barycentric representation [46, 63], and in the USA it sometimes appears as an exercise [42, 64].”
Spectral and High-Order Methods with Applications (2006, methodology): “Some MATLAB codes for spectral computations can be found in Trefethen[165]; the corresponding programs are available online at http://www.”
Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter (2008, positive): “Pseudospectral (PS) methods (see the books [40] or [41] for an introduction to the subject) are known as highly accurate solvers for partial differential equations (PDEs).”
Length scale and manufacturability in density-based topology optimization (2016, background): “, finding derivatives of any order, can be easily performed in the frequency domain [139].”