How to solve this system using ODE45?
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Seungman Kim
on 24 Mar 2017
Commented: Steven Lord
on 25 Jan 2020
The ODE system
dx/dt = -8/3 x + yz;
dy/dt = -10y + 10z;
dz/dt = -x*y + 28y - z when t=[0,50]
I only learned how to solve one equation each but,
I wanna solve this system using ODE45 on matlab
please help me how to make the script.
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Accepted Answer
Star Strider
on 24 Mar 2017
You first must assign ‘x’, ‘y’, and ‘z’ to a vector, then create the appropriate first-order differential equations with respect to each variable.
Example:
% % % MAPPING: x = v(1), y = v(2), z = v(3)
% dv(1,:) = -8/3.*v(1) + v(2).*v(3);
% dv(2,:) = -10*v(2) + 10*v(3);
% dv(3,:) = -v(1).*v(2) + 28*v(2) - v(3);
v_fcn = @(t,v) [-8/3.*v(1) + v(2).*v(3); -10*v(2) + 10*v(3); -v(1).*v(2) + 28*v(2) - v(3)];
ts = [0 50];
init_cond = [10; 10; 10];
[T,V] = ode45(v_fcn, ts, init_cond);
figure(1)
plot(T,V)
grid
I used an anonymous function here, simply for convenience. See the section on ‘Anonymous Functions’ in Function Basics for details on how to write them and use them.
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More Answers (1)
Sameer kumar nayak
on 25 Jan 2020
7d²x/dt²+3dx/dt+5x+6=0 how can we solve using matlab using ode45??
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Steven Lord
on 25 Jan 2020
See the "Nonstiff van der Pol Equation" example on this documentation page. You should be able to use the same techniques as that example to solve your ODE.
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