4- Examples

Example 1. (deformation of a shallow sphere cap)

Consider the following pair of second order differential equations:

subject to the boundary conditions

These equations describes the small finite deformation of a thin shallow sphere capof constant thickness subject to a quadratically varying axisymmetric external pressure distribution superimposed meridianal angle change of the deformed shell.

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Fig. 1, Example 1.

Example 2. (rotating flow of a incompressible fluid)

The following model describes the volocities in a boundary layer produced by the rotating flow of a viscous incompressible fluid over a stationary infinite disk

The solutions G and H oscillate, and it is difficult to find initial approximate solutions and meshes that lead to convergence of the nonlinear iteration. Also, the finite right end of the interval integration, L, which adequately represents infinity, increases with n.

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Fig. 2, Example 2.

Example 3. (ASturm-Liouville problem)

We consider the eigenvalue problem:


Figure :

Fig. 3, Example 3.

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