How to plot the first derivative of solution?

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Nauryzbay
Nauryzbay on 30 May 2023
Commented: Nauryzbay on 1 Jun 2023
function Piecewise1111copy
x1=1;
u=3;
global gamma1;
gamma1=x1;
teta=zeros(3,1);
teta(1)=0;
for i=1:3
teta(i+1)=2*i;
end
for j=1:1
for k=1:u%initial_func=[x1,x2];
[t,x] = ode45(@hop4,teta(k):0.0001:teta(k+1),x1(j));
n=length(t);
x1(j)=x(n,1);
gamma1=x1(j);
hold on
figure(1)
subplot(2,1,1);
plot(t,x(:,1),'color','g','Linewidth',1)
xlabel('$$t$$','interpreter','latex','fontsize',16); ylabel('$$y$$','interpreter','latex','fontsize',16);
hold on
subplot(2,1,2);
syms x(t);
y=diff(x,t);
fplot(y,[0,6],'color','g','Linewidth',1);
xlabel('$$t$$','interpreter','latex','fontsize',16); ylabel('$$\dot{y}$$','interpreter','latex','fontsize',16);
hold on
end
end
function dx=hop4(t,x)
global gamma1;
dx(1)=1+3*gamma1;

Answers (2)

James Tursa
James Tursa on 30 May 2023
After the ode45( ) call, simply pass your x solution through your derivative function to obtain the xdot values. You can either do this with a single call if your derivative function is vectorized, or you can do it in a loop.
  2 Comments
Steven Lord
Steven Lord on 30 May 2023
The fact that the ODE function uses a global variable (rather than passing additional parameters into the ODE function) likely will complicate that approach.
James Tursa
James Tursa on 30 May 2023
As ugly as that global variable is, I don't see it being changed during the derivative call, so I don't see how that complicates calling the derivative function right after the ode45( ) call to get the derivatives.

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Torsten
Torsten on 30 May 2023
Edited: Torsten on 30 May 2023
Piecewise1111copy()
function Piecewise1111copy
x1=1;
u=3;
teta=zeros(3,1);
teta(1)=0;
for i=1:3
teta(i+1)=2*i;
end
for j=1:1
for k=1:u%initial_func=[x1,x2];
[t,x] = ode15s(@(t,x)hop4(t,x,x1),[teta(k),teta(k+1)],x1);
hold on
figure(1)
subplot(2,1,1);
plot(t,x(:,1),'color','g','Linewidth',1)
xlabel('$$t$$','interpreter','latex','fontsize',16); ylabel('$$y$$','interpreter','latex','fontsize',16);
hold on
subplot(2,1,2);
for i=1:numel(t)
y(i) = hop4(t(i),x(i,:),x1);
end
plot(t,y,'color','g','Linewidth',1);
xlabel('$$t$$','interpreter','latex','fontsize',16); ylabel('$$\dot{y}$$','interpreter','latex','fontsize',16);
hold on
n=length(t);
x1=x(n,1);
end
end
end
function dx=hop4(t,x,x1)
dx(1)=1+3*x1;
end

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