Matlab help

[nadiaCegep]

Matlab can solve a set of non linear coupled equation; I want to find the third order solution, does anyone have a typical program for such Problem:
dx11/dt=a*x11*y12+b*y12
dy12/dt=c*y12*x11+d*x11
where a , b,c,d are constants
I want to see just the third order solution

 

[electricpete]

I'm not sure what you mean by 3rd order solution.

If you have initial values, you can solve by ode45.

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(2B)+(2B)' ?

 

[nadiaCegep]

a third order solution is when you develop ( like a series taylor for example); till the third order. I need the third order only. in this example, we can solve analytically using some approximation but i need the program to extend to my problem ( which is more complicated)

 

[LiteYear]

Did you find a solution?

It seems to me you have a non-linear, coupled, differential equation. But if you're only interested in a 3rd order polynomial solution, then you can evaluate the derivative, like so:

Let x11 = x(t), y12 = y(t).

Assume x(t) = A + Bt + Ct^2 and y(t) = D + Et + Ft^2.

Then your coupled equations are just:

B + 2Ct = a(A + Bt + Ct^2)(D + Et + Ft^2) + b(D + Et + Ft^2)
E + 2Ft = c(A + Bt + Ct^2)(D + Et + Ft^2) + d(A + Bt + Ct^2)

Expand and equate coefficients and you'll have 10 linear equations in 6 unknowns. Should be relatively easy to solve numerically from there.