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INF5620 Lecture: Analysis of finite difference schemes for diffusion processes
INF5620 Lecture: Analysis of finite difference schemes for diffusion processes
Hans Petter Langtangen [1, 2]
[1] Center for Biomedical Computing, Simula Research Laboratory
[2] Department of Informatics, University of Oslo
Dec 14, 2013
Table of contents
Analysis of schemes for the diffusion equation
Properties of the solution
Example
Visualization of the damping in the diffusion equation
Damping of a discontinuity; problem and model
Damping of a discontinuity; Backward Euler simulation
Damping of a discontinuity; Forward Euler simulation
Damping of a discontinuity; Crank-Nicolson simulation
Fourier representation
Analysis of the finite difference schemes
Analysis of the Forward Euler scheme
Results for stability
Analysis of the Backward Euler scheme
Stability
Analysis of the Crank-Nicolson scheme
Stability
Summary of accuracy of amplification factors; large time steps
Summary of accuracy of amplification factors; time steps around the Forward Euler stability limit
Summary of accuracy of amplification factors; small time steps
Observations
Analysis of schemes for the diffusion equation