second order partial differential element in an ODE
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Hi, Does anyone know who to write a script for the below equation?
z' = 1/L*[Ω Pctr *Vs *cos(Ωt)−(R +2∂L/∂u*v)*z−(1/c+ (∂^2 L)/(∂u^2 )v^2+ ∂L/∂u *v')*y].
The main concern is the second order partial differential element.
Thanks a lot.
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Walter Roberson
2011-9-3
Additionally, L, u, v, y and z are all functions of t.
Davis sent me a copy of the paper, but I do not know how to deal with the diff(L(t),u(t)) part.
Bjorn Gustavsson
2011-9-3
There must be something more relating z to some of u, v and y (L?)? Or some of them to make this a second order ODE.
Walter Roberson
2011-9-3
There is; Davis has shown only one of the equations here.
L(t) has a known exponential formula, but u(t) is defined through another differential equation.
There are two particular difficulties:
1) I do not know how to differentiate a function with respect to another function, diff(L(t),u(t))
2) because u(t) is being worked out numerically by an ode*() call (as u' is one of the equations), the formula for u(t) is not initially known, which makes differentiating with respect to u(t) suspect.
Bjorn Gustavsson
2011-9-3
Ok. I would (simplistically) start trying to make functions for dL/du and d^2L/du^2 - which should work if the OP just want to solve the ODE for one given L (or if L, dL/du, d^2L/du^2 is called with additional parameters). This might work if L doesn't show up in the LHS of the ODE - which would turn it into something else than an ODE...
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