How to plot the first derivative of solution?

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;

Answer 1

[James Tursa]

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.

[Steven Lord]

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]

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.

Answer 2

[Torsten]

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

[Nauryzbay]

Thank you so much.