shahid

Mr. skystar Pak

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8 years, 343 days

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These are questions asked by shahid

I draw a 3d graph and now i want the table of this graph. how can we get a table from the data of a plotted graph.

May grapg was obtained from the following commands

 

restart;
plot3d(1/2*(q^(2*n)-5.*q^n+(2.*q-1)^n+3), q = 2 .. 15, n = 2 .. 20);
 

TQ.mw

Can any one help for finding the solution of these differntial equations and then plotting the graph for differnt values of M

(FILE ATTACHED)
 

eqn1 := (R/(R-theta(eta))+Omega)*(diff(f(eta), `$`(eta, 3)))+f(eta)*(diff(f(eta), `$`(eta, 2)))+R*(diff(f(eta), `$`(eta, 2)))*(diff(theta(eta), eta))/(R-theta(eta))^2+Omega*(diff(g(eta), eta))+lambda*theta(eta)*Cos(alpha)-M*(diff(f(eta), eta))^2 = 0; eqn2 := (R/(R-theta(eta))+(1/2)*Omega)*(diff(g(eta), `$`(eta, 2)))-2*Omega*(2*g(eta)+diff(f(eta), `$`(eta, 2)))+(diff(f(eta), eta))*g(eta)+(diff(g(eta), eta))*f(eta)+R*(diff(g(eta), eta))*(diff(theta(eta), eta))/(R-theta(eta))^2 = 0; eqn3 := (1+`ε`*theta(eta))*(diff(theta(eta), `$`(eta, 2)))+`ε`*(diff(theta(eta), eta))^2+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+Q*theta(eta)+L*exp(-eta) = 0

(R/(R-theta(eta))+Omega)*(diff(diff(diff(f(eta), eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))+R*(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))/(R-theta(eta))^2+Omega*(diff(g(eta), eta))+lambda*theta(eta)*Cos(alpha)-M*(diff(f(eta), eta))^2 = 0

 

(R/(R-theta(eta))+(1/2)*Omega)*(diff(diff(g(eta), eta), eta))-2*Omega*(2*g(eta)+diff(diff(f(eta), eta), eta))+(diff(f(eta), eta))*g(eta)+(diff(g(eta), eta))*f(eta)+R*(diff(g(eta), eta))*(diff(theta(eta), eta))/(R-theta(eta))^2 = 0

 

(1+epsilon*theta(eta))*(diff(diff(theta(eta), eta), eta))+epsilon*(diff(theta(eta), eta))^2+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+Q*theta(eta)+L*exp(-eta) = 0

(1)

Omega := 2.; M := .5; R := 5; lambda := 20; `ε` := .2; Pr := 1; Q := .5; L := .5; W := .5; n := .1; alpha := (1/6)*Pi

bc := f(0) = W, (D(f))(0) = 0, (D(f))(infinity) = 0, (D(theta))(0) = -1, theta(infinity) = 0, g(0) = -n*(DD(f))(0), g(infinity) = 0

f(0) = W, (D(f))(0) = 0, (D(f))(N) = 0, (D(theta))(0) = -1, theta(N) = 0, g(0) = -n*(DD(f))(0), g(N) = 0

(2)

``


 

Download TQ.mw

 

How can i copy paste some differential equations with boundary conditions from maple work sheet to here

I m using the follwing commands for ploting the five differnt values of M

with(plots):
SDfd1 := odeplot(dsol[1], [eta, diff(f(eta), eta)], -1 .. 1, color = green, axes = box);
SDfd2 := odeplot(dsol[2], [eta, diff(f(eta), eta)], -1 .. 1, color = red, axes = box);
SDfd3 := odeplot(dsol[3], [eta, diff(f(eta), eta)], -1 .. 1, color = blue, axes = box);
SDfd4 := odeplot(dsol[4], [eta, diff(f(eta), eta)], -1 .. 1, color = black, axes = box);
SDfd5 := odeplot(dsol[5], [eta, diff(f(eta), eta)], -1 .. 1, color = pink, axes = box);
display([SDfd1, SDfd2, SDfd3, SDfd4, SDfd5], labels = ["η", "f ' (η)"],
    labeldirections = [horizontal, vertical], labelfont = [italic, 16], axes = boxed,
    axesfont = [times, 14], thickness = 3);

But i do not want in colors.....i need graph without colors in different styles. how can ? Moreover i need legend which must be in centre of graph or within the box. It must not on left, right ,up or below. can some one help ?

what does it means and what it will do. Can some one help me for solving this

Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);

while i m receiving the following message:

"Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received Shoot "

Full program is :

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots):
N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta),
        diff(fp(eta), eta) = fpp(eta),
        diff(fpp(eta), eta) = fppp(eta),
        diff(g(eta), eta) = gp(eta),
        diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta))*gp(eta)+2.*g(eta)*fp(eta)+2.*N2*N3*(m(eta)*np(eta)-n(eta)*mp(eta))),
        diff(m(eta), eta) = mp(eta),
        diff(mp(eta), eta) = Re_m*(m(eta)+(eta-2.*f(eta))*mp(eta)+2.*m(eta)*fp(eta)),
        diff(n(eta), eta) = np(eta),
        diff(np(eta), eta) = Re_m*(2.*n(eta)+(eta-2.*f(eta))*np(eta)+2.*N2/N3*m(eta)*gp(eta)),
        diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta))*fppp(eta)-2.*N2*N2*m(eta)*(diff(mp(eta), eta)))
       }:
   
blt := 1.0;
IC := { f(0) = 0,
        fp(0) = 0,
        fpp(0) = alpha1,
        g(0) = 1,
        gp(0) = beta1,
        m(0) = 0,
        mp(0) = beta2,
        n(0) = 0,
        np(0) = beta3,
        fppp(0) = alpha2
      };
BC := { f(blt) = .5,
        fp(blt) = 0,
        g(blt) = 0,
        m(blt) = 1,
        n(blt) = 1};
infolevel[shoot] := 1;
 

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