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Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Spectral_method> ?p ?o }

• Spectral_method abstract "Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, often involving the use of the Fast Fourier Transform. The idea is to write the solution of the differential equation as a sum of certain \"basis functions\" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the coefficients in the sum in order to satisfy the differential equation as well as possible.Spectral methods and finite element methods are closely related and built on the same ideas; the main difference between them is that spectral methods use basis functions that are nonzero over the whole domain, while finite element methods use basis functions that are nonzero only on small subdomains. In other words, spectral methods take on a global approach while finite element methods use a local approach. Partially for this reason, spectral methods have excellent error properties, with the so-called \"exponential convergence\" being the fastest possible, when the solution is smooth. However, there are no known three-dimensional single domain spectral shock capturing results (shock waves are not smooth). In the finite element community, a method where the degree of the elements is very high or increases as the grid parameter h decreases to zero is sometimes called a spectral element method.Spectral methods can be used to solve ordinary differential equations (ODEs), partial differential equations (PDEs) and eigenvalue problems involving differential equations. When applying spectral methods to time-dependent PDEs, the solution is typically written as a sum of basis functions with time-dependent coefficients; substituting this in the PDE yields a system of ODEs in the coefficients which can be solved using any numerical method for ODEs. Eigenvalue problems for ODEs are similarly converted to matrix eigenvalue problems.Spectral methods were developed in a long series of papers by Steven Orszag starting in 1969 including, but not limited to, Fourier series methods for periodic geometry problems, polynomial spectral methods for finite and unbounded geometry problems, pseudospectral methods for highly nonlinear problems, and spectral iteration methods for fast solution of steady state problems. The implementation of the spectral method is normally accomplished either with collocation or a Galerkin or a Tau approach.Spectral methods are computationally less expensive than finite element methods, but become less accurate for problems with complex geometries and discontinuous coefficients. This increase in error is a consequence of the Gibbs phenomenon.".
• Spectral_method wikiPageExternalLink pg=1083.
• Spectral_method wikiPageExternalLink bube.htm.
• Spectral_method wikiPageExternalLink 35198.
• Spectral_method wikiPageExternalLink BOOK_Spectral2000.html.
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• Spectral_method wikiPageLength "12664".
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• Spectral_method wikiPageRevisionID "640810132".
• Spectral_method wikiPageWikiLink Applied_mathematics.
• Spectral_method wikiPageWikiLink Burgers_equation.
• Spectral_method wikiPageWikiLink Calculus.
• Spectral_method wikiPageWikiLink Category:Numerical_analysis.
• Spectral_method wikiPageWikiLink Category:Numerical_differential_equations.
• Spectral_method wikiPageWikiLink Collocation_method.
• Spectral_method wikiPageWikiLink Computational_science.
• Spectral_method wikiPageWikiLink Convolution.
• Spectral_method wikiPageWikiLink Differential_equation.
• Spectral_method wikiPageWikiLink Discrete_element_method.
• Spectral_method wikiPageWikiLink Eigenvalues_and_eigenvectors.
• Spectral_method wikiPageWikiLink Elliptic_boundary_value_problem.
• Spectral_method wikiPageWikiLink Fast_Fourier_transform.
• Spectral_method wikiPageWikiLink Finite_element_method.
• Spectral_method wikiPageWikiLink Fourier_series.
• Spectral_method wikiPageWikiLink Galerkin_method.
• Spectral_method wikiPageWikiLink Gaussian_grid.
• Spectral_method wikiPageWikiLink Gibbs_phenomenon.
• Spectral_method wikiPageWikiLink Inner_product_space.
• Spectral_method wikiPageWikiLink Integration_by_parts.
• Spectral_method wikiPageWikiLink Kronecker_delta.
• Spectral_method wikiPageWikiLink M._Yousuff_Hussaini.
• Spectral_method wikiPageWikiLink Numerical_methods_for_ordinary_differential_equations.
• Spectral_method wikiPageWikiLink Ordinary_differential_equation.
• Spectral_method wikiPageWikiLink Orthogonality.
• Spectral_method wikiPageWikiLink Partial_differential_equation.
• Spectral_method wikiPageWikiLink Poissons_equation.
• Spectral_method wikiPageWikiLink Pseudo-spectral_method.
• Spectral_method wikiPageWikiLink Runge–Kutta_methods.
• Spectral_method wikiPageWikiLink Shock_capturing_method.
• Spectral_method wikiPageWikiLink Sine_wave.
• Spectral_method wikiPageWikiLink Smoothness.
• Spectral_method wikiPageWikiLink Spectral_element_method.
• Spectral_method wikiPageWikiLink Steven_Orszag.
• Spectral_method wikiPageWikiLink Tau_method.
• Spectral_method wikiPageWikiLink Viscosity.
• Spectral_method wikiPageWikiLinkText "Fourier spectral methods".
• Spectral_method wikiPageWikiLinkText "Spectral method".
• Spectral_method wikiPageWikiLinkText "spectral method".
• Spectral_method wikiPageWikiLinkText "spectral model".
• Spectral_method wikiPageWikiLinkText "wave based".
• Spectral_method wikiPageUsesTemplate Template:Citation_needed.
• Spectral_method wikiPageUsesTemplate Template:Cite_book.
• Spectral_method wikiPageUsesTemplate Template:More_footnotes.
• Spectral_method wikiPageUsesTemplate Template:Numerical_PDE.
• Spectral_method wikiPageUsesTemplate Template:Reflist.
• Spectral_method subject Category:Numerical_analysis.
• Spectral_method subject Category:Numerical_differential_equations.
• Spectral_method hypernym Techniques.
• Spectral_method type Weapon.
• Spectral_method type Algorithm.
• Spectral_method comment "Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, often involving the use of the Fast Fourier Transform.".
• Spectral_method label "Spectral method".
• Spectral_method sameAs Q2308831.
• Spectral_method sameAs Spektralmethode.
• Spectral_method sameAs Métodos_espectrales.
• Spectral_method sameAs روش‌های_طیفی.
• Spectral_method sameAs m.01k8b4.
• Spectral_method sameAs Q2308831.
• Spectral_method wasDerivedFrom Spectral_method?oldid=640810132.
• Spectral_method isPrimaryTopicOf Spectral_method.