# Question:How to get convergent solution of the shear flow problem?

## Question:How to get convergent solution of the shear flow problem?

Maple 2020

Hi,

Need your help to find the convergent solution of the attached problem.

Here is some information about parameters

(0 <= gamma <= 10,      0 <= rho & nu <= 200)

 > restart:
 > with(plots):
 > N:=6:
 >
 > eq1 :=3*diff(f(eta),eta,eta,eta)+2*f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta))^2;
 (1)
 >
 > eq2 := 3*nu*diff(g(eta),eta,eta,eta)+2*g(eta)*diff(g(eta),eta,eta)-(diff(g(eta),eta))^2;
 (2)
 >
 > bc:=f(0) = 0, g(0) = 0, D(f)(0) = D(g)(0), D(D(f))(0) = -rho*nu*D(D(g))(0), D(D(f))(6) = 1, D(D(g))(N) = gamma;
 (3)
 >
 > para:={nu=3, gamma=10};
 (4)
 >
 > A1 := dsolve(subs(para,rho=2, {bc, eq1, eq2}), numeric,method = bvp[midrich],maxmesh=12500, output=array([seq( 0.01*i, i=0..100*N)])):
 >
 > pf1 := odeplot(A1, [[eta,diff(f(eta),eta), linestyle = 1, color = blue]], 0 .. N):
 >
 > pf2 := odeplot(A1, [[eta,diff(g(eta),eta), linestyle = 3, color = red]], 0 .. N):
 > display({pf1,pf2}, axes = boxed,thickness=3,labels = [eta, "f' '"],labelfont = ["ROMAN", 22,Bold,Italic],axesfont = ["ROMAN", "ROMAN", 14,Bold],axis=[thickness=3]);