ODE Solver with array value parameter

Question

Teo Protoulis 2019-10-20

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/486467-ode-solver-with-array-value-parameter

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?

3 个评论
显示 1更早的评论隐藏 1更早的评论

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 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.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2019-10-21

5
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/486467-ode-solver-with-array-value-parameter#answer_397333

在 MATLAB Online 中打开

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