Prof. Vladimir A. Dobrushkin
This tutorial contains many matlab scripts.
You, as the user, are free to use all codes for your needs, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. Any comments and/or contributions for this tutorial are welcome; you can send your remarks to
The best way to plot direction fileds is to use existing m-files, credited to John Polking from Rice University (http://math.rice.edu/~polking/). He is the author of two special MATLAB routines: dfield8 plots direction fields for single, first order ordinary differential equations, and allows the user to plot solution curves; pplane8 plots vector fields for planar autonomous systems. It allows the user to plot solution curves in the phase plane, and it also enables a variety of time plots of the solution. It will also find equilibrium points and plot separatrices. The latest versions of dfield8 and pplane8 m-functions are not compatible with the latest Matlab version (R2015b). You can grab its modification that works from dfield.m
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- Shampine, L.F., Kierzenka, J., Reichelt, M.W., olving Boundary Value Problems for Ordinary Di erential Equations in Matlab with bvp4c, 2000.