bvp : A Nonlinear ODE Eigenvalue Problem.

This demo illustrates the location of eigenvalues of a nonlinear ODE boundary value problem as bifurcations from the trivial solution family. The family of solutions that bifurcates at the first eigenvalue is computed in both directions. The equations are

$$\begin{array}{cl} u_1 ' &= u_2 , \\ u_2 ' &=-(p_1 \pi)^{2}u_1 + u_1^{2} ,\end{array}$$ (15.3)

with boundary conditions $u_1(0)=0 , \quad u_1(1)=0.$   

Table 15.3: Commands for running demo bvp.

AUTO -COMMAND	ACTION
! mkdir bvp	create an empty work directory
cd bvp	change directory
demo('bvp')	copy the demo files to the work directory
run(c='bvp.1')	compute the trivial solution family and locate eigenvalues
sv('bvp')	save output-files as b.bvp, s.bvp, d.bvp
run(c='bvp.2',s='bvp')	compute the first bifurcating family. Constants changed : IRS, ISW, NPR, DSMAX
ap('bvp')	append output-files to b.bvp, s.bvp, d.bvp
run(c='bvp.3',s='bvp')	compute the first bifurcating family in opposite direction. Constants changed : DS
ap('bvp')	append output-files to b.bvp, s.bvp, d.bvp