A Short Course on Exponential Integrators: Construction, Analysis, and Implementation for Time Dependent Partial Differential Equations
June 15 @ 16:15 – 17:45
COURSE OVERVIEW
Exponential integrators are powerful numerical methods for solving time-dependent partial differential equations. This short course introduces the construction, analysis, and efficient implementation of exponential integrators, providing both theoretical foundations and practical insights.
We study linearization of semilinear and nonlinear evolution equations and develop modern exponential integration schemes. The course covers convergence theory and implementation issues, in particular the efficient computation of matrix-function–vector products using Krylov subspace methods.
The course is based on the classical review by Hochbruck & Ostermann (2010) and will also address more recent developments.
TOPICS
Linearization of semilinear and nonlinear evolution equations
Exponential Runge–Kutta methods
Exponential Rosenbrock-type methods
Convergence analysis and error estimates
The exponential Euler method – analysis and proof
Efficient implementation of matrix-function–vector products
Krylov subspace methods
Recent developments beyond the review by Hochbruck & Ostermann (2010)
SCHEDULE
Monday, June 15 14:15 – 15:45
Monday, June 15 16:15 – 17:45
Monday, June 22 16:15 – 17:45
VENUE
Hörsaal 3 (HS 3) MI Building Boltzmannstr. 3 TUM-Campus Garching
INTENDED AUDIENCE
Graduate students, doctoral researchers, and scientists interested in:
Numerical analysis
Scientific computing
Differential equations
Computational mathematics
REFERENCE
M. Hochbruck and A. Ostermann. Exponential Integrators. Acta Numerica, 19:209–286, 2010.
