Example 3.2.10 Blasius Equation - Infinite Domains
The Blasius problem is defined by:[22][12]
f
with the boundary conditions
f(0)=0 (3.3.25)
and
This boundary value problem is different from other boundary value problems discussed in this chapter because equation (3.2.24) is a third order ODE with three boundary conditions. In addition, the domain is semi-infinite. This boundary value problem is solved in Maple below by replacing ∞ in equation (3.2.27) by 10.
| > | restart: |
| > | with(plots): |
| > | eq:=f(eta)*diff(f(eta),eta$2)+2*diff(f(eta),eta$3); |
| (1) |
| > | BCs:=(f(0),D(f)(0),D(f)(10)-1); |
| (2) |
| > | sol:=dsolve({eq,BCs},{f(eta)},type=numeric); |
| (3) |
The solution for η = 0 and η = 10 are obtained as:
| > | sol(0); |
| (4) |
| > | sol(10); |
| (5) |
The solution obtained is plotted below:
| > | odeplot(sol,[eta,f(eta)],0..10,thickness=4,color=red,title="Figure Exp. 3.2.19.",axes=boxed); |
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| > | odeplot(sol,[eta,diff(f(eta),eta)],0..10,thickness=4,color=green,title="Figure Exp. 3.2.20.",axes=boxed); |
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| > |