# Question:plotting problem.

## Question:plotting problem.

Maple 16

This question was asked before but because of the curiosity, I

bring it in the light again. We have a system of odes

restart:with(plots):

a := 1; b := .5; d := 1; omega := .4; h1 := 1+a*cos(x); h2 := -d-b*cos(x+omega);

F := Q-1-d;

de:={alpha*(diff(f(y), y, y, y, y))+G*(diff(theta(y), y, y))+B*(diff(phi(y), y, y))

+6*beta*(diff(f(y), y, y))*(diff(f(y), y, y, y))^2+3*beta*(diff(f(y), y, y, y, y))*

(diff(f(y), y, y))^2 = 0,

diff(theta(y), y, y)+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0'

diff(phi(y), y, y)+Nb*(diff(theta(y), y, y))/Nt = 0,

f(1+cos(x)) = (1/2)*Q-1, f(-1-.5*cos(x+.4)) = -(1/2)*Q+1, (D(f))(1+cos(x)) = -1,

theta(-1-.5*cos(x+.4)) = 1, phi(-1-.5*cos(x+.4)) = 1, (D(f))(-1-.5*cos(x+.4)) = -1,

theta(1+cos(x)) = 0, phi(1+cos(x)) = 0}

d1 := subs(Nb = 7, Nt = 1, G = 2, B = 2, beta = .2, alpha = 2, [de]);

de1 := dsolve(d1, numeric,output=listprocedure):

param:={G = 2, B = 2, beta = .2, alpha = 2};

P1 := eval((alpha+3*beta*(diff(f(y), y, y))^2)*(diff(f(y), y, y, y))+G*theta(y)+B*phi(y),param);

P2:=subs(de1,P1);

P3:=evalf(Int(P2,0..1));

The question has two parts,

1. We need to have P1 interms of Q and x only.
2. Once we got P1(Q,x) then take Q fix and integrate P1 w.r.t x=0..1

But Q in part 2 should be treated in such a way that later on it can be used for plotting purpose.

Finally, I think what we want to achieve is to have a way to plot two types of results

1.     P1 vs x for fixed values of Q
2.     P3 v Q  (P3=Int(P1,x=0..1))

For convenience I have uploaded the maple sheet conatining all the equations.

Thanks

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