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Question: How to plot with numeric solution from dsolve

Question:How to plot with numeric solution from dsolve

Gabriel samaila 35 Maple 16
ode homework numeric differential-equations bvp plotting duplicate-question
May 15 2021
1

ishak.mw
 

> 

restart
> 

with*plots; -1; ode1 := diff(f(eta), eta, eta, eta)+(1/2)*f(eta)*(diff(f(eta), eta, eta)) = 0

diff(diff(diff(f(eta), eta), eta), eta)+(1/2)*f(eta)*(diff(diff(f(eta), eta), eta)) = 0

 (1)
> 

ode2 := (diff(theta(eta), eta, eta))/pr+3*N*f(eta)*(diff(theta(eta), eta))/(6*N+8) = 0

(diff(diff(theta(eta), eta), eta))/pr+3*N*f(eta)*(diff(theta(eta), eta))/(6*N+8) = 0

 (2)
> 

bcs1 := f(0) = 0, (D(f))(0) = S, (D(f))(16) = 1-S;

f(0) = 0, (D(f))(0) = S, (D(f))(16) = 1-S

 (3)
> 

fixedparameter := [pr = 1];

[pr = 1]

 (4)
> 

ode3 := eval(ode2, fixedparameter);

diff(diff(theta(eta), eta), eta)+3*N*f(eta)*(diff(theta(eta), eta))/(6*N+8) = 0

 (5)
> 

ode4 := eval(ode1, fixedparameter);

diff(diff(diff(f(eta), eta), eta), eta)+(1/2)*f(eta)*(diff(diff(f(eta), eta), eta)) = 0

 (6)
> 

bcs2 := theta(16) = 0, (D(theta))(0) = -a*(1-theta(0));

theta(16) = 0, (D(theta))(0) = -a*(1-theta(0))

 (7)

 

> 

L := [1, 5, 10]

[1, 5, 10]

 (8)
> 

 
  
> 

``
> 


  for k to 10 do
      sol_All := dsolve
                 ( eval
                   ( {bcs1, bcs2, ode3, ode4},
                     [N= L[k],a=1,S=1]
                   ),
                   [f(eta), theta(eta)],
                   numeric,
                   output = listprocedure
                 );
      Y_sol || k := rhs(sol_All[5]);
      YP_sol || k := -rhs(sol_All[6]);
feta || k := rhs(sol_All[4]);
      fpeta || k := rhs(sol_All[3])
  end do:

Error, invalid subscript selector

  
> 

for k to 10 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do

1, [HFloat(0.8022978364702027), HFloat(0.19770216352979716)]

  

5, [HFloat(0.7250508085648081), HFloat(0.27494919143519203)]

  

10, [HFloat(0.7099202264181006), HFloat(0.29007977358189907)]

  

Error, invalid subscript selector

  
> 

for k to 10 do L[k], [(feta || k)(0)] end do

1, [HFloat(-0.4437495989448031)]

  

5, [HFloat(-0.4437495983315978)]

  

10, [HFloat(-0.4437495982077529)]

  

Error, invalid subscript selector

  
> 

``
> 

  plot( [ seq((Y_sol||j)(eta), j = 1..16)],
         eta = 0 .. 10,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((feta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((fpeta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, fprime(eta)],
         axes = boxed
      );

Warning, expecting only range variable eta in expression Y_sol4(eta) to be plotted but found name Y_sol4

  

 

Warning, expecting only range variable eta in expression YP_sol4(eta) to be plotted but found name YP_sol4

  

 

Warning, expecting only range variable eta in expression feta4(eta) to be plotted but found name feta4

  

 

Warning, expecting only range variable eta in expression fpeta4(eta) to be plotted but found name fpeta4

  

 
> 

NULL
> 

``
> 

NULL


 

Download ishak.mw

Good day every one;

please im soliciting for a help on how to plot my Nusselt number and Skin friction.

The attached is plotting against the dependent variable (eta) but i want skin friction (f  ' ' ) against N or Pr not against eta 

thank you for your help in aticipation
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