non linear ordinary differential equations ?

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Tommy7571

Gast


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Verfasst am: 18.10.2018, 10:55 Titel: non linear ordinary differential equations ?

Hello,

I have a a system of 20 coupled nonlinear ordinary differential equations, each equation being of the type

dxi/dt =∑ ki*xi*xj

with i, j = 1 to 20 (and xi=xi(t) being the integrated function of dxi/dt).

As far as I understand, these equations are not linear ordinary differential equations anymore. They are also different from most equations I saw before.
To solve it, I tried lode45 but I got an error x(i) (=xi) out of bounds =1 after the first term. Since it is for linear differential equations, I suppose that no products of functions are aloud.
How can I solve this numerically with Octave?

Is there a solver available?

Thanks

Regards

Tommy7571

Tommy7571

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Verfasst am: 18.10.2018, 17:09 Titel: non linear ordinary differential equations ?

Hello,

In fact I thought it is a problem due to the non linear terms of my system but I was wrong. I could resolve the Robertson problem (online for matlab) using ode15s.

Code:

# y1' = -0.04'y1+10^4*y2*y3;
# y2' = 0.04*y1-10^4*y2*y3-3*10^7*y2^2
# y3' = 3E7*y2^2
#the conservation law is
# y'(1) + y'(2) + y'(3) = 0
#with initial conditions the conservation law is
# y(1) + y(2) + y(3) = 1

function dy = f(t,y)
#dy/dt = [0 ; 0 ; 0];
#dy(1)/dt = -0.04*y(1)+(10^4)*y(2)*y(3);
#dy(2)/dt = 0.04*y(1)-(10^4)*y(2)*y(3)-(3*10^7)*y(2)^2; #
#dy(3)/dt = 3E7*y(2)^2;

dy = [-0.04*y(1) + 1e4*y(2).*y(3) ; 0.04*y(1) - 1e4*y(2).*y(3) - 3e7*y(2).^2 ; y(1) + y(2) + y(3) - 1 ];
endfunction

Funktion ohne Link?

I gave a value for x(6)0 as initial value so the term is similar to that of the Robertson System . I did not give a mass conseration in the options by 'mass' is this obligatory?

Thanks

Regards

Tommy7571


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