ext : Spurious Solutions to BVB.

This demo illustrates the computation of spurious solutions to the boundary value problem

$$\begin{array}{cl} & u_1' - u_2 = 0 , \\ & u_2' + \lambda^2 \p... ... t \in [0,1], \\ & u_1(0) = 0, \quad u_1(1) = 0. \\ \end{array}$$ (19.2)

Here the differential equation is discretized using a fixed uniform mesh. This results in spurious solutions that disappear when an adaptive mesh is used. See the AUTO -constant IAD in Section 10.3. This example is also considered in BeDo:81 BeDo:81 and DoKeKe:91b DoKeKe:91b.

Table 19.2: Commands for running demo ext.

AUTO -COMMAND	ACTION
! mkdir ext	create an empty work directory
cd ext	change directory
demo('ext')	copy the demo files to the work directory
run(c='ext.1')	detect bifurcations from the trivial solution family
sv('ext')	save output-files as b.ext, s.ext, d.ext
run(c='ext.2',s='ext')	compute a bifurcating family containing spurious bifurcations. Constants changed : IRS, ISW, NUZR
ap('ext')	append output-files to b.ext, s.ext, d.ext