Advanced Discretization Methods

COURSE OBJECTIVES

At the end of the course, the student will be able to: - use the major concepts and results of spectral methods theory - plan and write computer code

COURSE DESCRIPTION
The course examines the development and analysis of spectral methods for the solution of time-dependent partial differential equations. Topics include key elements of approximation and stability theory for Fourier and polynomial spectral methods, as well as temporal integration and numerical aspects.

LEARNING METHODS
The course will use lectures, homework and reading assignments.

EXAMINATION INFORMATION
The course will be evaluated through homework, midterm and final exams

REFERENCES

• Spectral methods for time-dependent problems implementation, post-processing and error estimates; J. Hesthaven, S. Gottlieb, D. Gottlieb