"Sridatta Pasumarthy" <sridatta1988@gmail.com> wrote in message <ibv6s4$1k1$1@fred.mathworks.com>...
> how do i solve four complicated differential equations which have four variables? is ode23 the best possible operator i could be use?
>
> equations are 
>
> dw/dt = f(z) * dy/dt
> w * dx/dt = g(z) * dy/dt
> w * dy/dt = f(z) + g(z) * dx/dt + j(z) * dz/dt
> w * dz/dt = j(z) * dy/dt
>
> initial conditions are 
> x(0)=0, y(0)=0, z(0)=0, dx/dt(0)=0, dy/dt(0)=0, dz/dt(0)=v
>
> so as you see all four of them are interconnected and i need to plot the variation of 'dw/dz' vs 'z' at the end of the problem? i have been trying for some time and unable to find an answer....
         
Fortunately these equations are linear in the four derivatives, so you can find explicit expressions for each of the derivatives in terms of nonderivatives. According to my symbolic 'solve' these turn out to be:
dx/dt = f(z)*g(z)/(w(z)^2g(z)^2j(z)^2)
dy/dt = f(z)*w(z)/(w(z)^2g(z)^2j(z)^2)
dz/dt = f(z)*j(z)/(w(z)^2g(z)^2j(z)^2)
dw/dt = f(z)^2*w(z)/(w(z)^2g(z)^2j(z)^2)
These are in the form required by the 'ode' solvers.
I am puzzled by your initial conditions. If dz/dt(0) = v is nonzero, that would require that both f(0) and j(0) be nonzero. In turn dy/dt(0) = 0 would then imply that w(0) = 0. If w(0) is zero, then dw/dt(0) would also be zero. That means if I am not mistaken that w(t) would remain at a constant zero value, and in turn so would y(t).
Roger Stafford
