How to plot for a different initial values at same time

I need help how to plot for a different initial values of v0 at same time.

 if 
    zspan=[0,400];
   v0=[1;0.01;0.12;]; % Initial values 
% Creating a matrix 
zsol = [];
v1sol = [];
v2sol = [];
v3sol = [];
options=odeset('RelTol',1e-2,'AbsTol',1e-6,'Events',@events);
[t,v] = ode45(@(t,v)rhs(t,v), zspan, v0,options);
zsol =  [zsol;t];
v1sol = [v1sol;v(:,1)];
v2sol = [v2sol;v(:,2)];
v3sol = [v3sol;v(:,3)];
figure(1)
plot(abs(v1sol),zsol,'r')
xlabel('Volume Flux, V')
ylabel('Height, z')
grid on ; 
figure (2)
plot(abs(v2sol),zsol,'g')
xlabel('Momentum Flux, M')
ylabel('Height, z')
grid on ;
function [rho, Nsqr]=density1(z)
%%Data for density with respect to depth 
zval= [2 3 5 7 10 15 20 25 30 40 50 60 70 80 90 100 125 150 160 175 200 225 250 275 300 325 350 375 400];
rho1 = [17.2731684 17.1649375 21.43455647 22.4140625 23.86332207 24.3746967 24.70487685 24.6003125 24.8933125 25.42772826 26.03220776 26.439625 26.8151875 26.86830797 27.1949375 27.34406944 27.5551875 27.728625 27.23423729 27.88542857 27.752249049 28.1025 28.2415 28.37 28.05366667 28.6565 28.7755 28.898 29.013]; 
rho0=29;
g=9.8;
zvala=400-zval;
zvalue=fliplr(zvala);
rho2=fliplr(rho1);
rho3=smoothdata(rho2,'lowess',6);
rho=interp1(zvalue,rho3,z);
rho4=interp1(zvalue,rho3,z+0.1);
Nsqr=(-g./rho0).*(rho4-rho);
end
function parameters=rhs(z,v)
       [~,Nsqr]=density1(z); 
       alpha=0.116;

            dV= 2*alpha*sqrt(v(2));
            dM= (v(1).*v(3))./v(2);
            dF= -Nsqr.*v(1); 
   parameters=[dV;dM;dF];
  end

 function [value, terminate, direction] = events(t,v)
   value = v(1);
   terminate=1;
   direction=0; 
  end
end

Answer 1

[Torsten]

zspan=[0 400];
v0mat = [1 0.01 0.12;2 0.01 0.12;3 0.01 0.12;4 0.01 0.12];
options=odeset('RelTol',1e-2,'AbsTol',1e-6,'Events',@events);
for k=1:size(v0mat,1)
  v0=v0mat(k,:);
  [z,v]=ode45(@rhs,zspan,v0,options);
  zsol{k}=z;
  v1sol{k}=v(:,1);
  v2sol{k}=v(:,2);
  v3sol{k}=v(:,3);
end

If the assignment of the results to cell works this way (?), you can now plot the results.

Best wishes

Torsten.

[Dereje]

Hi Torsten, Yes it works I've just put the plot inside the loop.

hold on 
figure(1)
for k=1:size(v0mat,1)
plot(v1sol{k},zsol{k})
end

Thanks. You are always helpful!!

Answer 2

[Morteza Hajitabar Firuzjaei]

you can name both plot as figure(1)

Morteza Hajitabar Firuzjaei

[Dereje]

That is not what I meant. But I would like to see the plot for a different initial values for example for v1(of initial values)=1;1.5;2;2.5 by keeping v2 and v3(of initial values) constant.

[Morteza Hajitabar Firuzjaei]

i don't understand your goal! ask your question clearly

[Dereje]

 v0=[1;0.01;0.12;]; % Initial values

This is my initial values. But if I plot with these values, I only get one result for this specific initial values. So I wanted to have many initial values(may be using a loop) in different pattern like I said above. I think it is very clear now.

[Torsten]

Call ode45 in a loop, save the results from each run in a cell matrix and plot the results after MATLAB exited the loop.

Best wishes

Torsten.

[Dereje]

 I am getting errors. I defined it like you said. Is there any thing wrong with the initialization?    

 zspan=[0,400];
v0=[1:4;0.01;0.12;]; % Initial values 
% Creating a matrix 
N=5;
zsol = [];
v1sol = [];
v2sol = [];
v3sol = [];
options=odeset('RelTol',1e-2,'AbsTol',1e-6,'Events',@events);
[t,v] = ode45(@(t,v)rhs(t,v), zspan, v0(1:N),options);
for k=1:length(v0)
    [tN,vn] = ode45(@(t,v)rhs(t,v), zspan, v0(1:k),options);
end