initsys.m

This is similar to init.m. Each time you change the type of system or any of the associated parameters/conditions in the system, this file must be edited, saved, and initsys must be typed in the command window (or copy-and-paste at the Emporium).

t0, tf are the starting and ending times. They will generally be given with the problem.

x0vec is the vector containing the initial $x$-values for each equation in the system. They will generally be given with the problem.

initax is the plot window sizing vector only for use with pplane2d.m. The first two entries correspond to the desired $x_1$-range (horizontal). The second two entries correspond to the desired $x_2$-range (vertical).

A is the matrix of parameters associated with the linear part of the system.

B is the matrix of parameters associated with the nonlinear part of the sytem (if any).

x1symb is the symbolic solution $x_1(t)$ to the first equation in the system; e.g., if a system for a 2nd order ODE, x1symb is the symbolic solution to the ODE. It must be entered in single quotes.

x2symb is the symbolic solution $x_2(t)$ to the second equation in the system; e.g., if a system for a 2nd order ODE, x2symb is the symbolic solution to the first derivative $x'(t) = x_2(t)$. It must be entered in single quotes.

x1symb and x2symb are used for graphing, mainly with $2 \times 2$ systems.

eqn_name is the name of the MATLAB function M-file that describes the RHS of the system. It must be entered in single quotes AND without the .m extension.

symbolicplot is the type of plot desired in the lower-left of sys3plot. Choosing `solutions' will plot the symbolic solutions x1symb and x2symb wrt the time interval t0 to tf. Choosing `phase' will plot the two symbolic solutions x1symb and x2symb against each other in a phase plane plot. Choosing `eigenvals' will plot the eigenvalues of the matrix ${\tt A}$. Choosing '' will result in no plot in the lower-left. A choice is made by commenting out the others with a % at the beginning of each line containing the undesired options.

The rest of the entries in initsys.m remain the same for all systems and cases. They are not changed by the user.