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Science Forum Index » Math - Numerical Analysis Forum » Solving Parabolic non-linear PDE using MATLAB
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Message |
| Grazia |
 Posted: Wed Mar 21, 2007 7:22 am |
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Guest
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Hi guys
I need to solve a one-dimensional non linear parabolic PDE, using
MATLAB
PDE looks like this:
d(U^2)/dt = f(t)*d2(U^6)/dx2
I tried using pdepe.m function. However, this function requires a
certain format. Specifically:
C(x,t,u,du/dx)d(u)/dt = d[F(x,t,u,du/dx)]/dx+S(x,t,u,du/dx). Does
anyone have any idea how I translate my function to fit this format?
i.e. What are the function C,S and F that I need to input pdepe.m?
Thanks,
Grazia |
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| Peter Spellucci |
| Posted: Wed Mar 21, 2007 7:22 am |
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Guest
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In article <1174479720.669669.118750@b75g2000hsg.googlegroups.com>,
"Grazia" <dalgranati@hotmail.com> writes:
Quote: Hi guys
I need to solve a one-dimensional non linear parabolic PDE, using
MATLAB
PDE looks like this:
d(U^2)/dt = f(t)*d2(U^6)/dx2
I tried using pdepe.m function. However, this function requires a
certain format. Specifically:
C(x,t,u,du/dx)d(u)/dt = d[F(x,t,u,du/dx)]/dx+S(x,t,u,du/dx). Does
anyone have any idea how I translate my function to fit this format?
i.e. What are the function C,S and F that I need to input pdepe.m?
Thanks,
Grazia
d(U^2)/dt = 2*U*(dU/dt) => C(....)=2*U
d[F(x,t,u,du/dx)]/dx =
F_x + F_u*(du/dx) + F_{u_x} u_xx
and
f(t) d2(U^6)/dx2 = f(t)* d(6*U^5*U_x)/dx
=> F(t,x,u,u_x) = f(t)*6*U^5*U_x
F(t,x,u,v) = f(t)*6*u^5*v
hth
peter |
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| Janne Huttunen |
| Posted: Fri Mar 23, 2007 2:04 am |
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Hi Grazia,
I don't have a certain answer but something you could try. If f is
positive, you may set u=U^2 to get the equation
f(t)^-1 d(u)/dt = d2(u^3)/dx2=d[3u^2 du/dx]/dx
So you could choose
C(x,t,u,du/dx)=f(t)^-1
F(x,t,u,du/dx)=3u^2 du/dx
S=0
Grazia wrote:
Quote: Hi guys
I need to solve a one-dimensional non linear parabolic PDE, using
MATLAB
PDE looks like this:
d(U^2)/dt = f(t)*d2(U^6)/dx2
I tried using pdepe.m function. However, this function requires a
certain format. Specifically:
C(x,t,u,du/dx)d(u)/dt = d[F(x,t,u,du/dx)]/dx+S(x,t,u,du/dx). Does
anyone have any idea how I translate my function to fit this format?
i.e. What are the function C,S and F that I need to input pdepe.m?
Thanks,
Grazia
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