Solving Complex Coupled Differential Equations
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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
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Star Strider
2014-11-6
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:
1 个评论
Mohammad Abouali
2014-11-6
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?!
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Torsten
2014-11-6
0 个投票
I guess the legend is wrong.
Shouldn't it read
str = {'$$ x $$', '$$ \dot{x} $$', '$$ y $$', '$$ \dot{y} $$'};
?
Best wishes
Torsten.
1 个评论
Star Strider
2014-11-6
Correct. I reversed the legend accidentally after looking through the LaTeX documentation.
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