Hi, Im now trying to run my code. But it took like years to even getting the results. may I know any solutions on how to get faster results? Because I have run this code for almost 4 hours yet there is still 'Evaluating...' at the corner left. And when I tried to stop the program, it will stop at 'R1...'.

Digits := 18;
with(plots):n:=1.4: mu(eta):=(diff(U(eta),eta)^(2)+diff(V(eta),eta)^(2))^((n-1)/(2)):
Eqn1 := 2*U(eta)+(1-n)*eta*(diff(U(eta), eta))/(n+1)+diff(W(eta), eta) = 0;
Eqn2 := U(eta)^2-(V(eta)+1)^2+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(U(eta), eta))-mu(eta)*(diff(U(eta), eta, eta))-(diff(U(eta), eta))*(diff(mu(eta), eta)) = 0;
Eqn3 := 2*U(eta)*(V(eta)+1)+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(V(eta), eta))-mu(eta)*(diff(V(eta), eta, eta))-(diff(V(eta), eta))*(diff(mu(eta), eta)) = 0;
bcs1 := U(0) = 0, V(0) = 0, W(0) = 0;
bcs2 := U(4) = 0, V(4) = -1;
R1 := dsolve({Eqn1, Eqn2, Eqn3, bcs1, bcs2}, {U(eta), V(eta), W(eta)}, initmesh = 30000, output = listprocedure, numeric);
Warning, computation interrupted
for l from 0 by 2 to 4 do R1(l) end do;
plot1 := odeplot(R1, [eta, U(eta)], 0 .. 4, numpoints = 2000, color = red);

Thankyou in advance :)

Hi. I want to solve this system of equations by varying the value of n. I managed to aolve and plot for n=1, 1.1 and 1.2 but it happens to be a problem when I let n=1.3.

>restart;

>Digits := 15;

>with(plots):n:=1.3: mu(eta):=(diff(U(eta),eta)^(2)+diff(V(eta),eta)^(2))^((n-1)/(2)):

>Eqn1 := 2*U(eta)+(1-n)*eta*(diff(U(eta), eta))/(n+1)+diff(W(eta), eta) = 0;

>Eqn2 := U(eta)^2-(V(eta)+1)^2+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(U(eta), eta))-mu(eta)*(diff(U(eta), eta, eta))-(diff(U(eta), eta))*(diff(mu(eta), eta)) = 0;

>Eqn3 := 2*U(eta)*(V(eta)+1)+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(V(eta), eta))-mu(eta)*(diff(V(eta), eta, eta))-(diff(V(eta), eta))*(diff(mu(eta), eta)) = 0;

>bcs1 := U(0) = 0, V(0) = 0, W(0) = 0;

>bcs2 := U(20) = 0, V(20) = -1;

>R1 := dsolve({Eqn1, Eqn2, Eqn3, bcs1, bcs2}, {U(eta), V(eta), W(eta)}, initmesh = 30000, output = listprocedure, numeric);

Error, (in dsolve/numeric/bvp) precision is insufficient for required absolute error, suggest increasing Digits to approximately 23 for this problem

>for l from 0 by 2 to 20 do R1(l) end do;
>plot1 := odeplot(R1, [eta, U(eta)], 0 .. 20, numpoints = 2000, color = red);

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

I have tried increasing the Digits as suggested to 23, 25, 30, 31 up untill 500 yet still same error occur suggesting to increase the Digits. Is there any other way to solve this kind of error? Can someone help me? Thank you in advance.

Hi. I want to solve a system of equations. But I got this type of error. 

>restart;

>Digits := 15;
>with(plots):n:=0.7:Pr=1: mu(eta):=(diff(U(eta),eta)^(2)+diff(V(eta),eta)^(2))^((n-1)/(2)):
>Eqn1 := 2*U(eta)+(1-n)*eta*(diff(U(eta), eta))/(n+1)+diff(W(eta), eta) = 0:
>Eqn2 := U(eta)^2-(V(eta)+1)^2+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(U(eta), eta))-mu(eta)*(diff(U(eta), eta, eta))-(diff(U(eta), eta))*(diff(mu(eta), eta)) = 0:
>Eqn3 := 2*U(eta)*(V(eta)+1)+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(V(eta), eta))-mu(eta)*(diff(V(eta), eta, eta))-(diff(V(eta), eta))*(diff(mu(eta), eta)) = 0:
>Eqn4 := (W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(theta(eta), eta))-(mu(eta)*(diff(theta(eta), eta, eta))+(diff(mu(eta), eta))*(diff(theta(eta), eta)))/Pr = 0:
>bcs1 := U(0) = 0, V(0) = 0, W(0) = 0, theta(0) = 1:
>bcs2 := U(20) = 0, V(20) = -1, theta(20) = 0:
>R1 := dsolve({Eqn1, Eqn2, Eqn3, Eqn4, bcs1, bcs2}, {U(eta), V(eta), W(eta), theta(eta)}, initmesh = 20000, output = listprocedure, numeric);

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 8, got 7

>for l from 0 by 2 to 20 do R1(l) end do;
>plot1 := odeplot(R1, [eta, theta(eta)], 0 .. 20, numpoints = 2000, color = red);

What is the problem actually because based on the paper that I refer to, there is only 7 bc. 

Can anyone help me?

Thankyou in advance.