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Everything about Spectral method
Class of methods used in numerical analysis and scientific computing to solve ODE/PDE
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" and then to choose the coefficients in the sum in order to satisfy the differential equation as well as possible. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Spectral methodA 5-minute orientation
- Skim a recent paper: A facile method for Tauc exponent and corresponding electronic transitions determination in semiconductors directly from UV–Vis spectroscopy dataInfluential work since 2022
- Pick up a classic book: Spectrometric identification of organic compoundsThe most-reprinted book on the subject
- Read the landmark paper: Investigating Causal Relations by Econometric Models and Cross-spectral MethodsCited 17,623 times
- Go sideways: Finite element methodA closely related topic
- Go sideways: Sturm–Liouville theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Investigating Causal Relations by Econometric Models and Cross-spectral Methods
The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms
Spectral grouping using the nystrom method
Fractional Spectral Collocation Method
Spectral ratio method for measuring emissivity
The spectral moments method
Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems
Magnetar oscillations - II. Spectral method
🆕 Influential since 2022
A facile method for Tauc exponent and corresponding electronic transitions determination in semiconductors directly from UV–Vis spectroscopy data
Peak-fitting of Cu 2p photoemission spectra in Cu0, Cu1+, and Cu2+ oxides: A method for discriminating Cu0 from Cu1+
Debiasing Welch’s method for spectral density estimation
Multidomain spectral method for self-force calculations
FGC_SS: Fast Graph Clustering Method by Joint Spectral Embedding and Improved Spectral Rotation
📚 Books worth reading
Spectrometric identification of organic compoundsRobert M. Silverstein · 1963
Spectral/hp element methods for computational fluid dynamicsGeorge Karniadakis · 2005- 📕Three-dimensional marginal separationPeter W. Duck · 1988
- 📕Spectral and spectral-element methodsAnil E. Deane · 1997
Singular Spectrum Analysis for Time SeriesNina Golyandina, Anatoly Zhigljavsky · 2013- 📕A conservative staggered-grid chebyshev multidomain method for compressible flowsDavid A. Kopriva · 1995
- 📕A multi-domain spectral method for supersonic reactive flowsWai-Sun Don · 2002
- 📕Single-grid spectral collocation for the Navier-Stokes equationsChristine Bernardi · 1988
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical…
- Sturm–Liouville theory In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form ddx[p(x)dydx]+q(x)y=−λw(x)y…
- Numerical methods in fluid mechanics Fluid motion is governed by the Navier–Stokes equations, a set of coupled and nonlinear partial differential equations derived from the basic laws of conservati…
- Partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives…
- Helmholtz equation In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation:…
- Pseudo-spectral method Pseudo-spectral methods, also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and…
- Inverse scattering transform In mathematics, the inverse scattering transform (or nonlinear Fourier transform) is a method that solves the initial value problem for a nonlinear partial…
- Linear differential equation In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written…