Solving Complex Coupled Differential Equations

Hello,

My question is as follows. Say we have a set of coupled differential equations, such as

y'' = x' + y' + cos(y) and x'' = y'^2 + tan(y).

How would I go about implementing this with the regular ODE software? I understand how to solve coupled differential equations, and normal ODEs, but I've never had to deal with coupled differential equations with derivatives on both side.

Cheers

Answer 1

[Star Strider]

These are relatively straightforward. To use the ODE solvers however, they have to use the same variable, that requires that you keep track of what is x and what is y:

couplode = @(t,y) [y(2); y(4)^2 + tan(y(3)); y(4); cos(y(3)) + y(2) + y(4)];

[t,y] = ode45(couplode, [0 0.49*pi], [1;1;1;1]*1E-8); 

figure(1)
plot(t, y)
grid
str = {'$$ \dot{y} $$', '$$ y $$', '$$ \dot{x} $$', '$$ x $$'};
legend(str, 'Interpreter','latex', 'Location','NW')

produces this interesting plot:

[Mohammad Abouali]

why y and \dot{y} graph don't match? Clearly y is decreasing at some point so \dot{y} should be negative but it is always positive?!

Answer 2

[Torsten]

I guess the legend is wrong.

Shouldn't it read

str = {'$$ x $$', '$$ \dot{x} $$', '$$ y $$', '$$ \dot{y} $$'};

?

Best wishes

Torsten.

[Star Strider]

Correct. I reversed the legend accidentally after looking through the LaTeX documentation.