Integrate for a specific period of time

Please help me. I am trying to use Euler integration to integrate for 10 seconds with a step size of .01 seconds. Plot x versus time.

x(0) = 1

t=0:.01:10;
x0=1;
xdot=-2*(x^3)+sin(0.5*t)*x;
for t=0:0.01:10
    x=integrate(xdot,t,x0);
end
plot(t,x)

[Walter Roberson]

https://x-engineer.org/undergraduate-engineering/advanced-mathematics/numerical-methods/euler-integration-method-for-solving-differential-equations/

However you do not have a differential equation, so it is not obvious to me what Euler integration would have to do with the situation.

[Allison Bushman]

xdot is dx/dt

Answer 1

[Torsten]

t=0:.01:10;
x = zeros(numel(t));
x(1) = 1;
fun_xdot = @(t,x) -2*(x^3) + sin(0.5*t)*x;
for i = 1:numel(t)-1
    x(i+1) = x(i) + (t(i+1)-t(i))*fun_xdot(t(i),x(i));  
end
plot(t,x)

Answer 2

[Robert U]

Hi Allison,

you can use one of Matlab's integrated ODE solvers to solve your differential equation. The code below makes use of ode45.

t=0:.01:10;    % explicit time vector
x0=1;          % boundary condition

% define function containing my ODE
myODE = @(t,x) -2 .* x^3 + sin( 0.5 .* t) .* x;

% solve ODE with ode45
[tsol,xsol] = ode45(myODE,t,x0);

% plot result as explicit solution points
plot(tsol,xsol,'.')

Kind regards,

Robert