Reducing 2nd order ODE into coupled ODE. Solve using Euler Method and graph.

Hello, I'm trying to get a numerical solution for the given problem but I can't find a way to get it to work.

t0 = 0;
t = 5;
h = 0.1;
N = (t-t0)/h;
T = [t0:h:t;]';
Y = zeros(size(t));
Y(1) = 3;

%Start of Euler Method
syms y(t)
E = diff(y,2) + .1*diff(y) + .3*y == .02*y^3;
V = odeToVectorField(E)

for i = 1: N
   P = (V(2))
    Y(i+1) = Y(i) + h*P(i)
    S = Y(i+1)
end
plot(T,Y,'o')

the error I'm getting is the following:

The following error occurred converting from sym to double:

Unable to convert expression into double array.

Error in Euler (line 19)

Y(i+1) = Y(i) + h*P(i)

Answer 1

[Stephan]

tspan = [0 5]; % time span to integrate
y0 = [3 0]; % initial conditions

%Start of Euler Method
syms y(t)
E = diff(y,2) + .1*diff(y) + .3*y == .02*y^3;
V = odeToVectorField(E);
odefun = matlabFunction(V,'Vars',{'t','Y'});
[t,y] = ode45(odefun,tspan,y0);
plot(t,y,'o')

[Andres Cardenas]

Thank you, i do need the ODE 45. What about the Euler method? I still can't get it to work. Can you see what the problem is?

[Stephan]

The result of odeToVectorField is a symbolic expression. This can not be used in the way you want it.

[Andres Cardenas]

Ok, good to know. How can I make my ODE into an actual expression that I can use for Euler's? Thank you so much for helping me.