How do I use a for loop in my ode15s based code for shooting method and get multiple graphs?

I am using ode15s solver to solve a set of odes by shooting technique and obtain graphs of the solutions.

while trying to vary some parameters in the equations I have used a for loop.

But I am not getting the proper graphs.

How do I use the 'for' loop properly to get the accurate graphs.

Here in the code below I need to vary for three values of the 'lambda' parameter, so that I could obtain 3 different graphs in one figure

    function shooting_method
clc;clf;clear;
global lambda gama Pr Rd Lew Nb Nt Mn
gama=1;  
Mn=6;
Rd=0.1;
Pr=10;
Nb=0.3;
Lew=10;
Nt=0.3;
pp = [0.5 1 1.5];
for i=1:numel(pp)
    lambda = pp(i);
%lambda=0.5;
x=[1 1 1];
format long
options= optimset('Display','iter');
x1= fsolve(@solver,x);
end
end
function F=solver(x)
options= odeset('RelTol',1e-8,'AbsTol',[1e-8 1e-8 1e-8 1e-8 1e-8 1e-8 1e-8]);
[t,u] = ode15s(@equation,linspace(0,2),[0 1 x(1) 1 x(2) 1 x(3)],options)
%sol= [t,u];
s=length(t);
F= [u(s,2),u(s,4),u(s,6)];
%y1 = deval(u(0,:))
plot(t,u(:,2),'LineWidth',2);hold on %t,u(:,4));
end
function dy=equation(t,y)
global lambda gama Pr Rd Lew Nb Nt Mn
dy= zeros(7,1);
dy(1)= y(2);
dy(2)= y(3)*(y(3)^2+gama^2)/(y(3)^2+lambda*gama^2);
dy(3)= y(2)^2/3-(2*y(1)*y(3)*(y(3)^2+gama^2))/(3*(y(3)^2+lambda*gama^2))+Mn*y(2);
dy(4)= y(5);
dy(5)= -(2*Pr*y(1)*y(5))/(3*(1+Rd)) - (Nb*y(5)*y(7))/(1+Rd) - (Nt*y(5)^2)/(1+Rd);
dy(6)= y(7);
dy(7)= -((2*Lew*y(1)*y(7))/3)+ (Nt/Nb)*((2*Pr*y(1)*y(5))/(3*(1+Rd)) + (Nb*y(5)*y(7))/(1+Rd) + (Nt*y(5)^2)/(1+Rd));
end

[MINATI]

Dear naygarp

Can you share the question or the paper of whose this is the code

[e-mail]

Answer 1

[Torsten]

function shooting_method
clc;clf;clear;
global lambda gama Pr Rd Lew Nb Nt Mn
gama=1;  
Mn=6;
Rd=0.1;
Pr=10;
Nb=0.3;
Lew=10;
Nt=0.3;
pp = [0.5 1 1.5];
for i=1:numel(pp)
    lambda = pp(i);
    %lambda=0.5;
    x=[1 1 1];
    format long
    options= optimset('Display','iter');
    x1= fsolve(@solver,x);
    options= odeset('RelTol',1e-8,'AbsTol',[1e-8 1e-8 1e-8 1e-8 1e-8 1e-8 1e-8]);
    [t,u] = ode15s(@equation,linspace(0,2,20),[0 1 x1(1) 1 x1(2) 1 x1(3)],options)
    U(i,:,:)=u;
    T(i,:)=t;
end
plot(T(1,:),U(1,:,2),T(2,:),U(2,:,2),T(3,:),U(3,:,2))
end

[naygarp]

I get this error after modification, I think it is due the 'fsolve' line

    Undefined function or variable 'solver'.
Error in fsolve (line 230)
            fuser =
            feval(funfcn{3},x,varargin{:});

             Error in shooting_method_sci_rana (line 18)
x1= fsolve(@solver,x)

What do I feed in to 'folve'?

[Torsten]

Of course,you will have to run the above modified function "shooting_method" together with your two functions "solver" and "equation" from above.

[MINATI]

Dear naygarp

Can you share the question or the paper of whose this is the code

[e-mail]