ODE Solver with array value parameter

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Teo Protoulis
Teo Protoulis 2019-10-20
评论： Dihan Zou 2020-4-11
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?
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Teo Protoulis
Teo Protoulis 2019-10-21
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
Star Strider 2019-10-21
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.

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Star Strider
Star Strider 2019-10-21
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.
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Star Strider
Star Strider 2019-10-21
As always, my pleasure!
I very much appreciate your compliment!
Dihan Zou
Dihan Zou 2020-4-11
Amazingly talented method. Thank you both!!!

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