@mmcdara 

Thank you so much it is working. 

But for all values of M

how to find numerical values of diff(h(Theta,Theta) and diff(f(Theta,Theta) at Theta= Pi/4

@mmcdara 

Thank you for your answer

Actually, my problem is three-point boundary

f(-(1/4)*Pi) = 0, g(-(1/4)*Pi) = 0, h(-(1/4)*Pi) = 1, H(-(1/4)*Pi) = 1, f(0) = 1, h((1/4)*Pi) = 1, f((1/4)*Pi) = 0, g((1/4)*Pi) = 0, H((1/4)*Pi) = 1

please look at the pdf  which type of plots i need. new_paper_two_phase.pdf

i want to draw similar plots Ode_New_TWO_phase.mw

starting question i have seperated the boundary i have plotted the graphs and merged both but i m not getting similar graphs there is variations in the answers and plots.

i m giving the reference solved in matlab the boundary conditions are specified in PDF

f(±1)=0,g(±1)=0,f(0)=1,h(±1)=1,H(±1)=1

new_paper_two_phase.pdf

I have changed the boundary then graphs are comming but in base paper graphs having two phases -1 to 1 range

Ode_New_TWO_phase.mw

@C_R

This is the example i want to solve

@acer

How to draw Qz1a[j] versus gamma. At Y=0.5

I can able to draw 

Qz1a[j] versus Y for any value of gamma but reverse i am not able to draw.

Please hlep me to draw with other parameters also i will check once.

Thank you.

with(plots):
cols := [red, blue, black,green]:
 plotAA:= display
  ( [ seq
      ( odeplot
        ( Ans1[k],[gamma,Qz1a[k]],
          gamma=0..1,Y=0.5,
          color=cols[k]
        ),
        k=1..numelems(Q1Vals)
      )
    ],
    'axes'= 'boxed','linestyle' = 'solid',labels=[gamma,'Q'],size=[900,700]
  ):
if i kept like this getting error not able to evaluate

@acer

Thank you for your responce sir,

I have another  question

for any value of Y i.e, Y=0.5,

How to write plot commond for Qz1a[j] versus gamma( range of gama from 0 to 1) for different values of Q1

And Thetabz1a[j] versus gamma.

ode_Plots_1_ac.mw

 @SHIVAS 

substituted all the equations, then also no change in the final expressions. 

If any related questions please tag i will check how to impliment they implimented

I have some more equation in the worksheet how to evaluate Q and Thetab terms.

can we substitute P1=(D1*ga+C1)/(1+ga) and P2= (D1-C1)/(1+ga), Z1= -(N*(C1-D1)^2 )/(1+ga)^2,

because the solution is getting long. to reduce the length of equation by substitution with appendixed term

MaplePrimes_ODE_problem.mw

@C_R

I have checked with those posts sir.

There is no answers for this type of questions.

Thank you

@KIRAN SAJJAN

Download sachi_stream_error_3d_ac.mw

How u got that plot directly. I m not getting sir

There sre two different  cases in one it is f(eta) and another is f1(eta)

All equation are ode equations after evaluation of f(eta)

Product with x values   for that need the 3d for x=0..1 and eta =0..10

3d_sachin_p1.mw

In this it is different  for two different parameters nussueslt number plot i need. In work shhet not showing any error but not getting the plot 

@SHIVAS

I also trying for similar graph. Give the solution for this type of problems

It will be helpfull for every one

Thank you

@acer  but i have small dought

for some parameter values Phid, Thetad, diff(Phi(eta,t),eta), diff(Theta(eta,t),eta), remains constant 

for Phid also remains constant for R values  i have tried for others parameters also giving single value for different values of parameters like Kp , Rd 

But in plot it is varing with different parameters error_in_table_value.mw

At pr =7 remains are same as mentioned in above u(y, t)

Horizonatal is y and verticle is t

y= 0..10 and t=0..1 

sir u can keep  y=0 and t=0.5 

i want same plots as mentioned by this person  

I m not getting  some points what u are asking. u can give the plot for that person worksheet only i will understand and according to that i will modify my equations 

thank you

At pr =7 remains are same as mentioned in above u(y, t)

Horizonatal is y and verticle is t

y= 0..10 and t=0..1