The equation dx/dt = F(x) can be linearized using Calerman techniques and solved with linear state equation method. But for some condition I found a proper decomposition of F(x) relating to know logist solution od a foundamental canonical problem .
What exactly are you trying to say? That you have found something which you cannot tell us about?
I can show but it is in handwritten form but i can send these work if you have some example to give me
Igor> in quadratures
I assume x and F are vectors, x and F. Or? (It is unsurprising that the logistic equation can give a good description of the flow between two fixpoints in the one-dimensional case, after a little rewriting).
Giuseppe> Calerman techniques
I also assume Calerman is a misprint for Carleman(?).
Yes Carleman , x can be a vector I followed Kowalsky Steeb work with some different approach . I am not a matematicians I am an electronic engineering.
Autonomous equation is considered as
dy/dt=f(y), y(t_0)=y_1;
to find the largest t-interval in which there exists a solution;
There is a particular point regarding autonomous equations and
autonomous equations depend only on y and not on t, it turns out that solutions to autonomous equations can be “translated” left or right. So the interval of existence is only dependent on how far we go from the initial starting point, not on where we started.
A real problem:
Let a particle be moving on real plane (y-t PLANE); Its law of motion is that: “the rate of change of the height of the particle from t-axis is equal to the square of the height from t-axis ” Assume that at t=0, the height is 1; Question be asked the particle will be in the real-plane throughout the maximum time interval ? Its a problem of Autonomous equation connected with reality
(equation is: dy/dt= y^2) Y(0)=1; ans : [0,1) when t is the time and positive;
Bonjour Abderrahim,
Je t'envoie un programme qui ressemble au script p14.m du livre de Trefethen et qui utilise la méthode du point fixe.
Bonne réception.
I am applying non linear first order ODe to train flow analysis in subway . Third order equation arises and I have trouble to solve. The coupling of dinamiv and electric supply is the next job I need to handle.
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