problem in solving such an equation
Hi, I have problem in solving such an equation
dy/dt=u(t)S(r)*[1+(dy/dr)^2] where u(t)=U[1+Vsin(w*t)] We are solving for y(r) and U is an constant =37, V >1. S(r)=S*(ra)^(1/3) and S is also constant =3.33. Follwing time depedent boundary conditions is used. dy/dt=0 if u(t)>=S(a) dy/dr=0 if u(t)<=S(a) I do not have problem when I solve this equations when V<1. Also I do not have problem when S(r)=S even if V>1. Please help me thanks 
Re: problem in solving such an equation
What kind of numerical scheme are you using to solve the problem ?
Harish 
Re: problem in solving such an equation
Actually I have used CN, Fully implicit and expilcit with back differencing and central differencing schemes.

Re: problem in solving such an equation
Have you tried to write down the analytic solution  your pde is only first order so you can write down a general expression for the characteristics  from which you should see the source of your problem!
Also isn't S(a)=0 your boundary condition so that dy/dt = 0 on r=a (I assame r=a is the boundary from your notation). 
Re: problem in solving such an equation
I have tried the analytic solutions of such equation. The analytic solution is only possible for the case of V<<1. But the case of V>1 analytical solution is wrong.
Can you give me examples how can analytical solutions helps in such case. Yes you are write about the boundary condition. R 
Re: problem in solving such an equation
I'm not sure what you mean by the analytic solution being wrong  unless you mean you tried to obtain a series solution in V<<1? Otherwise the (correct) analytic solution cannot be wrong since it is the solution to the equation!
What I meant by anaytic solution was that you can reduce your pde, using the method of characteristics, to a set of odes for dt/ds, dr/ds, dy/ds dp/ds and dq/ds where p=dy/dt, q=dy/dr and s is the variable along the characteristic. The analytic solution helps for two reasons: (1) It gives something to test your numerics against and (2) If there is a problem with the existence of the solution (i.e. finite time blowup) then you will be able to see why and in what parameter regions it happens. 
All times are GMT 4. The time now is 23:42. 