Topics in Differential Equations
- Math 934: Topics in Differential Equations
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University of Nebraska-Lincoln, spring 2017
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Syllabus
Course Documents
- Matlab Intro [pdf]. My introduction to Matlab worksheet.
- talk.pdf. My slides about Fourier transforms and PDEs.
- Logistic Worksheet [pdf]. My code for the logistic problem: logisticChaos.m
- Runge-Kutta Project [pdf] My n-dimensional rk4 code rk4_ndim.m and rk4_error.m code.
- A backward Euler solver: backward_euler.m which requires a Newton's method solver: Newton.m
- The Discrete Fourier Transform [pdf] A write-up by Prof. Steven Johnson about how the DFT is used to compute derivatives.
- FFTderivatives.m My code to compute derivatives using the FFT.
- FFT Theory [pdf] A write-up on the (correct!) algorithm to compute the FFT.
- heatProject.pdf My code for the logistic problem: heat_rk4.m
- Link to John Bowman's slides on dealiasing. [pdf]
- burgersProject.pdf (Code will be posted after all projects are in.)
- IMEX.pdf A discussion of mixed implicit/explicit methods.
- Read page 15 and Section 2.3. If you need more mathematical background, read chapter A, starting on page 225.
- transport_naive.m My code to "simulate" the transport equation with the (unstable) Euler method.
- transport_lf.m My code to simulate the transport equation with the leap-frog method.
- wave_lf.m My code to simulate the wave equation with the leap-frog method.
- Project_FEM_Poisson.pdf A project to code a 1D Poisson solver in Matlab.
"Think twice, code once." -Anonymous
