ODE Solver with array value parameter

I need to solve the following differential equations:

where x1 and x2 are the states of the system and y is the input of the system and it is represented by a 1002x1 vector. How is it possible to solve this system of differential equations?

[Daniel M]

How is this question related to MATLAB?

[Teo Protoulis]

I am trying to solve it using Matlab ode45(@ode, timespan, [0 0]) solver. My problem is that I can't find out how to pass each value of the vector y to the ode solver function . I mean take the first value y(1) of vector y and use for the step with initial values [0 0] for [x1 x2] , then the second value y(2) of vector y for the updated values of [x1 x2] and do this for all values of vector y.

[Star Strider]

What you describe is not the correct approach, in part because MATLAB uses adaptive ODE solvers, not fixed-step ODE solvers.

See my Answer for the correct approach.

Answer 1

[Star Strider]

Try this example:

yv = randn(1002,1);                                                                             % Create ‘y’
tv = 0:numel(yv)-1;                                                                             % Create Corresponding Time Vector

Eqns = @(t,x,tv,yv) [x(2)-interp1(tv(:), yv(:), t);  -3*x(2)-2*x(1)+3*interp1(tv(:), yv(:), t)];

tspan = linspace(0, 10, 50);
ic = [0; 1];                                                                                    % Use The Correct Initial Conditions
[T, X] = ode45(@(t,x)Eqns(t,x,tv,yv), tspan, ic);

figure
plot(T, X)
grid

Provide your own vectors for ‘y’ (that I call ‘yv’ here) and the time vector (‘tv’ here) that corresponds to it.

Make other appropriate changes to reflect the actual values you intend to use.

[Teo Protoulis]

You can't imagine how much you helped me. It works perfectly. Thank you very much!

[Star Strider]

As always, my pleasure!

I very much appreciate your compliment!

[Dihan Zou]

Amazingly talented method. Thank you both!!!