How to solve coupled differential equation in a limited range of the variable?

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Chinmay Sharma 2017-6-10

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https://ww2.mathworks.cn/matlabcentral/answers/344164-how-to-solve-coupled-differential-equation-in-a-limited-range-of-the-variable

评论： Star Strider 2017-6-18

采纳的回答： Star Strider

I need to solve the following set of coupled equations.(these are not the exact equations,but a similar example)

x'=y+x;

y'=2x+y+p;

where

p = y-7 if y>7

= 0 else

I dont know what type they fall into. I have tried using 'dsolve' but to no avail. Any specific matlab function for this case, or even a link to solving such equations would be greatly appreciated.

Thanks in advance.

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Karan Gill 2017-6-10

Did you try the numeric ode solvers?

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Star Strider 2017-6-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/344164-how-to-solve-coupled-differential-equation-in-a-limited-range-of-the-variable#answer_270284

在 MATLAB Online 中打开

This seems to work:

y = linspace(0,10);
p = (y-7).*(y>7);
figure(1)
plot(y, p)
grid
% % % MAPPING: x = z(1),  y = z(2)
de = @(t,z) [z(2) + z(1); 2*z(1) + z(2) + (z(2)-7).*(z(2)>7)];
ts = [0 10];
[T,Z] = ode15s(de, ts, [0.1; 0]);
figure(2)
semilogy(T, Z)
grid

Numerical ODE solvers tend not to do well with discontinuities. That does not seem to be a problem here, probably because ‘p’ is not a ‘step’ or other abrupt discontinuity.