non : A Non-Autonomous BVP.

This demo illustrates the continuation of solutions to the non-autonomous boundary value problem

$$\begin{array}{cl} u_1 ' &= u_2 , \\ u_2 ' &= -p_1 e^{x^3 u_1} , \\ \end{array}$$ (15.5)

with boundary conditions $u_1(0)=0 , \quad u_1(1)=0.$ Here $x$ is the independent variable. This system is first converted to the following equivalent autonomous system :

$$\begin{array}{cl} u_1 ' &= u_2 , \\ u_2 ' &= -p_1 e^{u_3^3 u_1} , \\ u_3 ' &= 1 , \\ \end{array}$$ (15.6)

with boundary conditions $u_1(0)=0 , \quad u_1(1)=0, \quad u_3(0)=0.$ (For a periodically forced system see demo frc).

Table 15.5: Commands for running demo non.

AUTO -COMMAND	ACTION
! mkdir non	create an empty work directory
cd non	change directory
demo('non')	copy the demo files to the work directory
run(c='non.1')	compute the solution family
sv('non')	save output-files as b.non, s.non, d.non