spiral

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1091_2020/spiral/spiral.html

spiral, discusses reaction-diffusion equations, the approximation of the Laplacian, the treatment of several kinds of boundary conditions, and finishes with an equation whose solution will grow into a spiral.

The notes:

• spiral.pdf
• spiral.tex

The original project description (a more up-to-date version is described in the spiral.pdf notes above):

• spiral_project.pdf

Useful codes.

• rms_norm.m, returns the root-mean-square (RMS) norm of a matrix or vector.

Skeletons: These are partial programs that you can use to carry out the exercises. Usually, there are some missing pieces of code, sometimes indicated by a question mark.

• skeleton1.m
• skeleton2.m
• skeleton3.m
• skeleton4.m
• skeleton5.m
• skeleton6.m, an outline for hw10.

Exercises: Look at these after you have tried to do the work on your own.

• exercise1.m, estimate the Laplacian in a 1D periodic region.
• exercise2.m, estimate the Laplacian in a 2D periodic region.
• exercise3.m, solves the 1D Fisher's equation dudt=duxx+u*(1-u).
• exercise3.png, a plot of the last solution.
• exercise4.m, solves the 1D Allen-Cahn reaction-diffusion equation with insulated ends.
• exercise4.png, a plot of the last solution.
• exercise5.m, solves the 2D Gray-Scott reaction-diffusion equation.
• exercise5.png, a plot of the last solution.

Homework: My version posted after you have turned yours in.

• hw10.m, solve a 2D reaction-diffusion equation whose solution grows into a spiral.
• hw10.png, a plot of the spiral solution.

Images:

• spiral.png, a plot that suggests the relationship between spiral lines and the velocity field in a fluid flow.