int : Boundary and Integral Constraints.

This demo illustrates the computation of a solution family to the equation

$$\begin{array}{cl} u_1 ' &= u_2 , \\ u_2 ' &= -p_1 e^{u_1} , \\ \end{array}$$ (15.2)

with a non-separated boundary condition and an integral constraint:

$$u_1(0)-u_1(1)-p_2=0 ,\qquad \int_0^{1}u(t)dt-p_3=0 .$$

The solution family contains a fold, which, in the second run, is continued in two equation parameters.

Table 15.2: Commands for running demo int.

AUTO -COMMAND	ACTION
! mkdir int	create an empty work directory
cd int	change directory
demo('int')	copy the demo files to the work directory
run(c='int.1')	1st run; detection of a fold
sv('int')	save output-files as b.int, s.int, d.int
run(c='int.2',s='int')	2nd run; generate starting data for a curve of folds. Constants changed : IRS, ISW vspace0.2cm
sv('t')	save the output-files as b.t, s.t, d.t
run(c='int.3',s='t')	3rd run; compute a curve of folds; restart from s.t. Constants changed : IRS vspace0.2cm
sv('lp')	save the output-files as b.lp, s.lp, d.lp