How to solve multi-variable system of ODEs

Question

2Lindsay2 2018-10-3

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https://ww2.mathworks.cn/matlabcentral/answers/422073-how-to-solve-multi-variable-system-of-odes

回答： Torsten 2018-10-4

I want to solve a system of 4 nonlinear ODEs with two variables x and y. I'm using the code below to try to achieve the solution.

 g = @(t, x, y) [
    gamma2/2/pi*((x(1)-x(2)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2));
    gamma1/2/pi*((x(2)-x(1)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2));
    gamma2/2/pi*(-(y(1)-y(2)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2));
    gamma1/2/pi*(-(y(2)-y(1)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2))
 ];
 [t, x, y] = ode45(g, [0 200], [y1_0 y2_0 x1_0 x2_0]);

Where gamma1, gamma2, y1_0, y2_0, x1_0, and x2_0 are constants.

Is there a way to use two variable like this? Or do I have to simplify the expression further by assigning y1 = x(1), y2 = x(2), x1 = x(3), x2 = x(4)?

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Answer 1

Torsten 2018-10-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/422073-how-to-solve-multi-variable-system-of-odes#answer_339689

在 MATLAB Online 中打开

[t z] = ode45(@(t,z)g(t,z,gamma1,gamma2), [0 200], [y1_0 y2_0 x1_0 x2_0]);
function dz = g(t,z,gamma1,gamma2)
y = z(1:2);
x = z(3:4);
dz = [gamma2/2/pi*((x(1)-x(2)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2));
      gamma1/2/pi*((x(2)-x(1)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2));
      gamma2/2/pi*(-(y(1)-y(2)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2));
      gamma1/2/pi*(-(y(2)-y(1)) / ((x(1)-x(2))^2 + (y(1)-y(2))^2))];