# How to plot for a different initial values at same time

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Dereje on 30 Jan 2018
Commented: Dereje on 30 Jan 2018
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

Torsten on 30 Jan 2018
Edited: Torsten on 30 Jan 2018
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 on 30 Jan 2018
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

you can name both plot as figure(1)
Morteza Hajitabar Firuzjaei
Dereje on 30 Jan 2018
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