Spectral Methods in Matlab

NumericalMethods in Engineering withMATLAB is a text for engineer- ing students and a reference for practicing engineers, especially those who wish to explore the power and efficiency ofMATLAB. The choice of numerical methods was based on their…

This is to review some recent progress in PDE. The emphasis is on (energy) supercritical nonlinear Schr"odinger equations. The methods are applicable to other nonlinear equations.

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in…

Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book…

We apply polynomial approximation methods - known in the numerical PDEs context as spectral methods - to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on a…

Trigonometric spectral methods can be very accurate for solving periodic problems on rectangular domains. They obtain their answers by sam- pling the input function on a grid. This article shows how spectral methods can be extended to the situation…

Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class…

A very common problem in science and engineering is the determination of the effects of uncertainty or variation in parameters and data on the output of a deterministic nonlinear operator. For example, such variations may describe the effect of…

We review the current state of Fourier and Chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations. Throughout the discussion we emphasize recent…

Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically,…