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TMA4320
Introduction to Scientific Computation
Polynomial interpolation
Polynomial interpolation: Error theory
Summary
Numerical integration: Interpolatory quadrature rules
Numerical integration: Composite quadrature rules
Summary
Numerical solution of ordinary differential equations
Numerical solution of ordinary differential equations: Euler’s and Heun’s method
Numerical solution of ordinary differential equations: Error analysis of one step methods
Numerical solution of ordinary differential equations: Higher order Runge-Kutta methods
Numerical solution of ordinary differential equations: Error estimation and step size control
Numerical solution of ordinary differential equations: Stiff problems
A modelling/simulation mini-project: The SIR model and some extensions
Summary
The Discrete Fourier Transform and its applications
The discrete Fourier transform
Trigonometric interpolation and friends
Using the discrete Fourier transform
Numerical differentiation and spectral derivatives
Solving PDEs with the Fourier spectral method in 2D
A Fourier spectral solver for the heat equation
Image processing using the Fast Fourier Transform
Exercises on the discrete Fourier transform
Summary for Chapter 5
Project 3: Simulation of phase separation in a binary mixture
Task 1: A first closer look at the Cahn-Hilliard equation
Task 2: A spectral solver for the biharmonic equation
Task 3: A spectral solver for the transient biharmonic equation
Task 4: A first IMEX solver for the Cahn-Hilliard equation
Task 5: A more sophisticated IMEX solver for the Cahn-Hilliard equation
Task 6: Simulation of phase separation phenomena
Bibliography
Repository
Open issue
Index
