Spectral Collocation Methods For Semilinear Problems
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Spectral Collocation Methods
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Author : M. Y. Hussaini
language : en
Publisher:
Release Date : 1987
Spectral Collocation Methods written by M. Y. Hussaini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
A Spectral Collocation Method For The Navier Stokes Equations
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Author : M. R. Malik
language : en
Publisher:
Release Date : 1984
A Spectral Collocation Method For The Navier Stokes Equations written by M. R. Malik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Navier-Stokes equations categories.
Solving Nonlinear Parabolic Partial Differential Equations Using Multidomain Bivariate Spectral Collocation Method
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Author : Motsa Sandile Sydney
language : en
Publisher:
Release Date : 2016
Solving Nonlinear Parabolic Partial Differential Equations Using Multidomain Bivariate Spectral Collocation Method written by Motsa Sandile Sydney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
In this study we introduce the multidomain bivariate spectral collocation method for solving nonlinear parabolic partial differential equations (PDEs) that are defined over large time intervals. The main idea is to reduce the size of the computational domain at each subinterval to ensure that very accurate results are obtained within shorter computational time when the spectral collocation method is applied. The proposed method is based on applying the quasi-linearization technique to simplify the nonlinear partial differential equation (PDE) first. The time domain is decomposed into smaller nonoverlapping subintervals. Discretization is then performed on both time and space variables using spectral collocation. The approximate solution of the PDE is obtained by solving the resulting linear matrix system at each subinterval independently. When the solution in the first subinterval has been computed, the continuity condition is used to obtain the initial guess in subsequent subintervals. The solutions at different subintervals are matched together along a common boundary. The examples chosen for numerical experimentation include the Burger's-Fisher equation, the Fitzhugh-Nagumo equation and the Burger's-Huxley equation. To demonstrate the accuracy and the effectiveness of the proposed method, the computational time and the error analysis of the chosen illustrative examples are presented in the tables.
Spectral Methods For Time Dependent Problems
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Author : Jan S. Hesthaven
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-11
Spectral Methods For Time Dependent Problems written by Jan S. Hesthaven and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-11 with Mathematics categories.
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Conforming Chebyshev Spectral Collocation Methods For The Solution Of Laminar Flow In A Constricted Channel
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Author : Institute for Computer Applications in Science and Engineering
language : en
Publisher:
Release Date : 1990
Conforming Chebyshev Spectral Collocation Methods For The Solution Of Laminar Flow In A Constricted Channel written by Institute for Computer Applications in Science and Engineering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Numerical Analysis Of Spectral Methods
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Author : David Gottlieb
language : en
Publisher: SIAM
Release Date : 1977-01-01
Numerical Analysis Of Spectral Methods written by David Gottlieb and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Technology & Engineering categories.
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Pseudospectral Collocation Methods For Fourth Order Differential Equations
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Author : National Aeronautics and Space Adm Nasa
language : en
Publisher: Independently Published
Release Date : 2018-10-17
Pseudospectral Collocation Methods For Fourth Order Differential Equations written by National Aeronautics and Space Adm Nasa and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-17 with Science categories.
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain. Malek, Alaeddin and Phillips, Timothy N. Unspecified Center NAS1-19480; RTOP 505-90-52-01
A Spectral Multidomain Method For The Solution Of Hyperbolic Systems
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Author : Institute for Computer Applications in Science and Engineering
language : en
Publisher:
Release Date : 1986
A Spectral Multidomain Method For The Solution Of Hyperbolic Systems written by Institute for Computer Applications in Science and Engineering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Spectral And High Order Methods For Partial Differential Equations
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Author :
language : en
Publisher:
Release Date : 1990
Spectral And High Order Methods For Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Pseudospectral Collocation Methods For Fourth Order Differential Equations
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Author : Alaeddin Malek
language : en
Publisher:
Release Date : 1994
Pseudospectral Collocation Methods For Fourth Order Differential Equations written by Alaeddin Malek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.