MATLAB: Trying to plot numerical solutions for systems of DEs

ode45systems of equations

I am having trouble using ode45 to do this is it says that my function is not a column vector but I don't know why it isn't.

f = @(t,x) [-2*x + 4*y; x + 2*y]

tspan = [0 5]

x0 = [0;0]

[t,x] = ode45(f,tspan,x0)

plot(t,x,'-o')

Error using odearguments (line 93)

@(T,X)[-2*X+4*Y;X+2*Y] must return a column vector.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in prac (line 5)

[t,x] = ode45(f,tspan,x0)

Best Answer

The reason is that ‘y’ is not defined in your function.

One option is to code ‘x’ as ‘x(1)’ and ‘y’ as ‘x(2)’:

f = @(t,x) [-2*x(1) + 4*x(2); x(1) + 2*x(2)];
tspan = [0 5];
x0 = [0;0]+eps;
[t,x] = ode45(f,tspan,x0);
figure
plot(t,x,'-o')

That works, and may do what you want.

Related Solutions

MATLAB: Anonymous function in ode45: column vector error

You are not calling ‘xdot’ correctly in your ode45 call.

Try this:

t = 0:.01:20;
x0 = [0 0]' + eps;
xdot = @(t,x) [0 1; 0 0] * x;
[T,X] = ode45(xdot,t,x0)
figure
plot(T, X)
grid

Also, the result is uniformly zero, so to prevent that, I added eps to ‘x0’.

MATLAB: How to solve this ODE 1000 times with random variables

You coded your differential equation correctly. Your ‘x’ variable has only two elements, so you cannot use ‘n’ (or ‘k’) to subscript them.

See if this does what you want:

n = 1000;
result = cell(n,1);
for k=1:n
    tspan=[1 7];A0=rand;P0=rand;g=rand;p=rand;B=rand;
    [t,x] = ode45(@(t,x) [-g*x(1) + p*x(1); -x(1)*x(2)+ B*x(2)], tspan, [A0 P0]);
    result{k} = x;
end

Note that because the time vector can change between your ode45 calls, a cell array is most appropriate. If you want a specific number of values to be returned each iteration, define ‘tspan’ as a vector of more than two elements.

Best Answer

Related Solutions

MATLAB: Anonymous function in ode45: column vector error

MATLAB: How to solve this ODE 1000 times with random variables

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