After running the code for (f ') w.r.t x , we need to draw( f ' ) w.r.t G (in X-axis) while varying n=0, 0.5, 1

function main
Pr=1;K=1;L=-1;S=0.1;
n=input('n=');
a=linspace(0,6,100);
G=linspace(0,7,100);
solinit=bvpinit(a,G,[0 1 0 1 0 0 1]);
sol=bvp4c(@ode,@bc,solinit);
xint=a;
sxint=deval(sol,xint);
function res=bc(ya,yb,G)
res=[ya(1)-S; ya(2)-L; ya(4)+n*ya(3); ya(6)-1; yb(2)-1; yb(4); yb(6);];        
end 
function dydx=ode(x,y,G)    
dydx=[y(2); y(3);(y(2)^2-1-y(1)*y(3)-K*y(5)-G*(1-y(2)))/(1+K);y(5);2*(y(2)*y(4)-y(1)*y(5)+K*(2*y(4)+y(3)))/(2+K);y(7);-Pr*y(1)*y(7)];             
end
plot(xint,sxint([2],:),'Linewidth',2);    %for f'
xlabel('\eta'); 
ylabel('f^\prime');
hold on
end

ERROR occurs as:

n=0

Error using bvparguments (line 108)

Error in calling BVP4C(ODEFUN,BCFUN,SOLINIT):

The derivative function ODEFUN should return a column vector of length 100.

Error in bvp4c (line 130)

bvparguments(solver_name,ode,bc,solinit,options,varargin);

Error in (line 7)

sol=bvp4c(@ode,@bc,solinit);

Answer 1

[Walter Roberson]

your G is length 100. You pass it to bvpinit so matlab knows that your ode function works with 100 derivatives. but your ode only returns 7 rather than 100.

I notice that your upper bound for G is 7, the same number as the derivatives calculated . I wonder if perhaps you used linspace incorrectly .

[MINATI]

Thanks Walter

After changing

G=linspace(0,3,10);

Error is :

Error using bvparguments (line 108)

Error in calling BVP4C(ODEFUN,BCFUN,SOLINIT):

The derivative function ODEFUN should return a column vector of length 10.

Error in bvp4c (line 130)

bvparguments(solver_name,ode,bc,solinit,options,varargin);

Error in (line 8)

sol=bvp4c(@ode,@bc,solinit);

I'm worried what to do now

[madhan ravi]

Could you post the latex form of your equations? Would be better if you provide the question asked.

[MINATI]

Dear Madhan

Latex form is attached

I have considered G for GAMMA, L for LAMBDA

[Walter Roberson]

Why are you using linspace() at all there?

[MINATI]

Since i want to vary G in X-axis, after variation w.r.t x

[MINATI]

Dear Walter

could we proceed here

[Walter Roberson]

No. Your problem appears to be unsolvable.

In order to be solvable, your guess of initial conditions (second parameter to bpvinit, length 100 or perhaps length 10) would have to be the same length as the number of values output by your ode function (11 in this case.)

If your G is to vary in X axis, then it sounds as if you are working on a 2D grid of locations. bvp4c is not typically usable for those situations: those are typically PDE problems.

[MINATI]

For ref another example

http://dx.doi.org/10.1016/j.asej.2015.04.006

Using eqns: (11,12) with B.Cs (13), completely odes are solved. Look at Fig.s (9, 10)

[Walter Roberson]

2D sheets call for the PDE Toolbox.

[MINATI]

actually I am not getting your point

2D sheets call for the PDE Toolbox.

[Walter Roberson]

pde Toolbox

You are doing finite element calculations in 2 dimension . The pde Toolbox has the routines needed for those kinds of tasks .

[MINATI]

Can I run pde toolbox, means I have to learn how to run this first or what to do?

[Walter Roberson]

You need the PDE Toolbox instead of what you are doing. You will have to learn how to use it.