@mmcdara Lot of thanks for your comments.

Your commends are working well, but I have some truble to get a values of a1, a2, a3 (Is it possible to consider a1 = a, a2 = b, a3 = c). How to find these values.

Also, I tried to solve for alpha = -48 degree, I have an error (see. Error.mw).

Kindly check the errors...

@mmcdara Thank you for your responses.
One more question... Is it possible to plot a f' function for various values of Pr such as 6, 7, 8, 9, 10

@C_R Thanks for your commends..

I have attached my problem through Difference.mw

@acer I have a excel data foo.xls for the values of x and f'(x)
I want to incert this excel sheet in maple plot a graph for f'(x).

@acer Thanks for your comments.
Is is possible to plot a data in the excel?

if it is possible... How to plot a multi-plot graph for different alpha values..

Thanks in advance...

@Carl Love Thanks for yous response...

Is it possible to plot a graph with respect to alpha. That means x axis has values -90 degree to +90 degree and y axis has values of f(x) or f(0)

@mmcdara Thansk for your response....

I could not download your file, there are some server isuue. Kindly resend it.
 

Is it possible to plot a graph with respect to alpha. That means x axis has values -90 degree to +90 degree and y axis has values of f(x) or f(0)...

@Preben Alsholm Thanks for your response.

I solved this porblem in numerically. I want a solutions in finite difference method

@Mariusz Iwaniuk thanks a lot!
It is possible to solve this problem in RK method?
Kindly concern my requirments....

@dharr Thanks a lot... Its working

@Thomas Richard
 M1.mw

@Thomas Richard thanks for your response.. It is working, but I have an error when tried to ploting

y(x):=eA(t).B+int(v(x)*eA(x-t)*theta(t-x),0..1);

You have any possiblities to solve this issue....

@Carl Love Thank you for your response. Your comments are very useful... I got a result

proc(x_bvp)  ...  end;
sol(0);
print(`output redirected...`); # input placeholder
                             sol(0)

But cannot get a solution How to find a solution.

It is possible to solve this equations to any other numerical method?

I used infinity = 10, but result is

Error, (in dsolve/numeric/bvp) Newton iteration is not converging

@C_R Thak you for your response...

The expression of equation has been rewritten by

((D@@2)(theta))(eta) = -(-D[t]*epsilon*(-gamma+beta)*(D(theta))(eta)+beta*(D[B]*epsilon*(mu-lambda)*(D(phi))(eta)+(1/2)*nu*(f(eta)*sin(alpha)+eta*cos(alpha))))*(D(theta))(eta)/(beta*sigma)

and removed the extra argument

Le = nu/D[B]

How to simplify this problem?

@Rouben Rostamian  Thank you for your response....

I attached my worksheet with correct form of equatons and initial and boundary conditons.

Kindly solve this...PDE_system.mw