Advanced Discretization Methods

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.

RECOMMENDED COURSES

Introduction to Ordinary Differential Equations, Introduction to Partial Differential Equations

REFERENCES

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