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Question: change the axis

Question:change the axis

shakuntala 25 Maple 13
plot axis
October 27 2016
0

> restart;

with(plots);

pr := .72; p := 0; n := [.5, 1, 1.5]; s := 0; a := .2; b := 0; L := [red, blue, green]; l := 0; k := 1;

for j to nops(n) do R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n);

sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2) = 0, diff(diff(theta(eta), eta), eta)+pr*k*f(eta)*(diff(theta(eta), eta))+R2*pr*k*(diff(f(eta), eta))*theta(eta)+(2*(a*(diff(f(eta), eta))+b*theta(eta)))/(1+n[j]) = 0, f(0) = 1, (D(f))(0) = b*((D@@2)(f))(0), (D(f))(1.8) = 0, theta(0) = 1+s*(D(theta))(0), theta(1.8) = 1], numeric, method = bvp);

fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = L[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = L[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(tplt[j], j = 1 .. nops(n))]);

 

staganation_point1.mw
 

can we chage the axis sir ?? like  f'' vs eta to f'' vs lambda.

``

> 

restart
> 

l := 1:

1

  

1.5

  

.5

  

[blue, green, red, yellow]

 (1)
> 

``
> 

for j to nops(p) do R1 := 2*n/(n+1); R2 := 2*p[j]/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed) end do:

 

 
> 

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

 
> 

sol1(0)

sol1(0)

 (2)
> 

sol1(.1)

[eta = .1, f(eta) = 1.05958091104306206, diff(f(eta), eta) = .643210624614908300, diff(diff(f(eta), eta), eta) = .881482678165403044, theta(eta) = .623284688471349546, diff(theta(eta), eta) = -.578039450700496560]

 (3)
> 

sol1(.2)

[eta = .2, f(eta) = 1.12800452943200891, diff(f(eta), eta) = .722346769554029544, diff(diff(f(eta), eta), eta) = .706526135439307756, theta(eta) = .568123251856343492, diff(theta(eta), eta) = -.525530979400813946]

 (4)
> 

sol1(.3)

[eta = .3, f(eta) = 1.20351830506746449, diff(f(eta), eta) = .785511903074783246, diff(diff(f(eta), eta), eta) = .561442941644520022, theta(eta) = .518103974464032668, diff(theta(eta), eta) = -.475257424178228970]

 (5)
> 

sol1(.4)

[eta = .4, f(eta) = 1.28466826824405134, diff(f(eta), eta) = .835505660630676662, diff(diff(f(eta), eta), eta) = .442470716586289281, theta(eta) = .472985640642506311, diff(theta(eta), eta) = -.427567049032814172]

 (6)
> 

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

 (7)
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sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

 (8)
> 

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

 (9)
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Download staganation_point1.mw

 

 

 

 

 
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