BOYD CHEBYSHEV AND FOURIER SPECTRAL METHODS PDF
Completely revised text focuses on use of spectral methods to solve Chebyshev and Fourier Spectral Methods: Second Revised Edition By: John P. Boyd. Chebyshev and Fourier Spectral Methods. Article (PDF Available) · October with Reads. Export this citation. John. Philip Boyd at University of Michigan. Chebyshev and Fourier Spectram Methods by John P. Boyd First edition (out of print), Springer-Verlag (), pp. Second edition, Dover, New York (), .
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Chebyshev and Fourier Spectral Methods
These notes evolved from a course I have taught the past five years to an audience drawn from half specyral dozen different disciplines at the University of Michigan: With such a diverse audience, this book is not focused on a particular discipline, but rather upon solving differential equations in general. The style is not lemma-theorem-Sobolev space, but algorithms- guidelines-rules-of-thumb.
Although the course is aimed at graduate students, the required background is limited. It helps if the reader has taken an elementary course in computer methods and also has been exposed to Fourier series and complex variables spetral the undergraduate level.
However, even this background is not absolutely necessary. Chapters 2 to 5 are a self- contained treatment of basic convergence and interpolation theory. The Best Books of Check out the top books of the year on our page Best Books of Product details Format Paperback pages Dimensions x x Looking for beautiful books? Visit our Beautiful Books page and find dpectral books for kids, photography lovers and more.
Other books bojd this series. Stochastic Approaches in Earthquake Engineering Y. Optimum Design of Structures L. Table of contents 1. Spedtral of Basis Functions. Comparison with Finite Element Methods. Non-Interpolating and Pseudospectral Families of Methods.
An Upper Chfbyshev on the Truncation Error. Asymptotic Calculation of Coefficients: Model Functions for Fourier Series. Convergence Theory for Chebyshev Polynomials. Functions with Singularities at the Endpoints.
Mean Weighted Residual Methods. General Properties of Basis Functions: Properties of Basis Functions: Galerkin’s in Quantum Theory: Galerkin’s Method via Gaussian Quadrature. The Envelope of the Interpolation Error. Whittaker Cardinal or “Sinc” Functions. Cardinal Functions for Trigonometric Interpolation.
Cardinal Functions for Orthogonal Polynomials. Pseudospectral Methods for Boundary Value Problems. Choice of Basis Set. The Cardinal Function Basis. Special Problems of Higher Dimensions: Special Problems in Higher Dimensions: Symmetry Classes for Trigonometric Functions. Differential Equations with Variable Coefficients.
Chebyshev & Fourier Spectral Methods : John P. Boyd :
Partial Summation in Two or More Dimensions. The Fast Fourier Transform. Endpoint versus Interior Singularities. Splitting and Its Cousins.
Chebyshev and Fourier Spectral Methods: Second Revised Edition – John P. Boyd – Google Books
Analytical and Numerical Background. Operator Theory of Time-Stepping Methods. Splitting the Navier-Stokes Equation. Fractional Step-Coupling Boundary Conditions.
Case Studies of Time Integration. Stellar Convection in Annular Shell: Plasma Physics in a Torus Fusion Reactor: Plane Poiseuille and Couette Flow: Complex Geometry and Variable Coefficients: Iterative Methods for Solving Matrix Equations. Stationary One-Step Iterative Methods.
The Many Uses of Coordinate Transformation. The General Theory of Coordinate Transformations. Mapping and Infinite and Fouurier Intervals. Eigenvalue Problems with Interior Singularities: Detours in the Complex Plane.
Methods for Unbounded Intervals. Whittaker Cardinal or “Sinc” Expansions. Algebraically Mapped Chebyshev Polynomials: Behavioral versus Numerical Boundary Conditions. Numerical Examples for Rational Chebyshev Functions: Rational Chebyshev Functions on y? Chebyshev Methods on a Semi-Infinite Xhebyshev. The Rational Chebyshev Function: Icosahedral Grids and the Radiolaria. Spherical Harmonics and Boyf. Alternatives to Spherical Harmonics: Transformation of the Horizontal Velocities.
Cylindrical, Toroidal and Polar Coordinates. An Illustration of Triangular Truncation. Special Basis Functions, I: Special Basis Functions, II: Analytical Applications and Symbolic Manipulation.
Tau-Approximation for a Epectral Function. Tau-Method for Differential Equations. The Weak Coupling of Elemental Solutions: Patching versus Variational Formalism. The Influence Matrix Method. A Bestiary of Basis Functions. Flow Chart on Choice of Basis Functions.
Block and “Bordered” Matrices: Global Methods for Linear Eigenvalue Problems: Operation Counts for Banded Matrices. Evaluating the Second Derivatives for the Hessian Matrix. Convexity, Positive Definiteness, and Conditions for a Minimum. Approximations that Depend Nonlinearly on the Free Parameters.
Nonlinear Approximation to the KdV Soliton: Book ratings by Goodreads. Goodreads is the world’s largest site for readers with over 50 million reviews.