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Lecture Spectral Methods, Summer Semester 2012

Spectral Methods for Partial Differential Equations

Dr. Maciek Korzec


Wednesday, 2-4pm in MA 542

Every two weeks, Thursday 12-2pm in MA 542

Besides popular numerical schemes, such as finite difference methods and finite element methods, spectral methods are another important tool for numerically solving partial differential equations. With these methods one gains spectral accuracy if the solutions are sufficiently smooth - a faster convergence rate than with any local polynomial based interpolation method.

In this lecture collocation and Galerkin methods based on trigonometric and Chebychev interpolants are introduced. Algorithms are developed to numerically solve nonlinear partial differential equations. Theoretical aspects, such as stability, convergence, spectral accuracy, but also implementation aspects for short, simple, fast MATLAB codes will be discussed. The theory is supported with many examples from fluid and solid material modeling.

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