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From: trung trinh on 10 Apr 2010 04:21
I have problem. We have equation system below
du1/dt = u2 and du2/dt = d(du/dx)/dx

with initial conditions
u1(x,0) = 0 , u2(x,0) = 0
boundary conditions
u1(0,t) = 0 , u2(0,t) =0
u1(1,t) =0 , u2(1,t) =0

I used command pdepe to solve this problem, and my code is:

///////////////////////////////////////////////////////////////////////////
function pdex1
m = 0;
x = [0:0.05:1];
t = [0:0.1:2];


sol = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);
u1 = sol(:,:,1);

figure
%plot(u1);
surf(x,t,u1);
title('u1(x,t)')
xlabel('Distance x')
ylabel('Time t')

% --------------------------------------------------------------
function [c,f,s] = pdex1pde(x,t,u,DuDx)
c = [1 0; 0 1];
f = [0 0; 1 0] * DuDx;
s = [u(2); 0];

% --------------------------------------------------------------
function u0 = pdex1ic(x)
u0 = [0; 1];
% --------------------------------------------------------------
function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t)
pl = [ul(1); ul(2)];
ql = [0; 0];
pr = [ur(1); ur(2)];
qr = [0; 0];
//////////////////////////////////////////////////////////////////////////

But have error:

??? Error using ==> daeic12 at 77
This DAE appears to be of index greater than 1.

Help me. Thank a lot.
From: Torsten Hennig on 10 Apr 2010 02:26
> I have problem. We have equation system below
> du1/dt = u2 and du2/dt = d(du/dx)/dx
>

I think you mean du2/dt = d/dx(du1/dx)

> with initial conditions
> u1(x,0) = 0 , u2(x,0) = 0
> boundary conditions
> u1(0,t) = 0 , u2(0,t) =0
> u1(1,t) =0 , u2(1,t) =0
>

That's easy - the solution is u1=u2=0 for all times t.
(From what you programmed below I think you meant
u2(x,0) = 1 :-) ).

Furthermore, you don't need boundary conditions for u1 - it's an ordinary differential equation.

> I used command pdepe to solve this problem, and my
> code is:
>
> //////////////////////////////////////////////////////
> /////////////////////
> function pdex1
> m = 0;
> x = [0:0.05:1];
> t = [0:0.1:2];
>
>
> sol = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);
> u1 = sol(:,:,1);
>
> figure
> %plot(u1);
> surf(x,t,u1);
> title('u1(x,t)')
> xlabel('Distance x')
> ylabel('Time t')
>
> %
> ------------------------------------------------------
> --------
> function [c,f,s] = pdex1pde(x,t,u,DuDx)
> c = [1 0; 0 1];
> f = [0 0; 1 0] * DuDx;
> s = [u(2); 0];
>
> %
> ------------------------------------------------------
> --------
> function u0 = pdex1ic(x)
> u0 = [0; 1];
> %

Set u0(2) to 0 if x equals 1.
Otherwise initial conditions and boundary conditions
are not consistent (which often causes the error from
below).


> ------------------------------------------------------
> --------
> function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t)
> pl = [ul(1); ul(2)];
> ql = [0; 0];
> pr = [ur(1); ur(2)];
> qr = [0; 0];
> //////////////////////////////////////////////////////
> ////////////////////
>
> But have error:
>
> ??? Error using ==> daeic12 at 77
> This DAE appears to be of index greater than 1.
>
> Help me. Thank a lot.


Best wishes
Torsten.
From: Torsten Hennig on 11 Apr 2010 22:55
> > I have problem. We have equation system below
> > du1/dt = u2 and du2/dt = d(du/dx)/dx
> >
>
> I think you mean du2/dt = d/dx(du1/dx)
>
> > with initial conditions
> > u1(x,0) = 0 , u2(x,0) = 0
> > boundary conditions
> > u1(0,t) = 0 , u2(0,t) =0
> > u1(1,t) =0 , u2(1,t) =0
> >
>
> That's easy - the solution is u1=u2=0 for all times
> t.
> (From what you programmed below I think you meant
> u2(x,0) = 1 :-) ).
>
> Furthermore, you don't need boundary conditions for
> u1 - it's an ordinary differential equation.
>
> > I used command pdepe to solve this problem, and
> my
> > code is:
> >
> >
> //////////////////////////////////////////////////////
>
> > /////////////////////
> > function pdex1
> > m = 0;
> > x = [0:0.05:1];
> > t = [0:0.1:2];
> >
> >
> > sol = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);
> > u1 = sol(:,:,1);
> >
> > figure
> > %plot(u1);
> > surf(x,t,u1);
> > title('u1(x,t)')
> > xlabel('Distance x')
> > ylabel('Time t')
> >
> > %
> >
> ------------------------------------------------------
>
> > --------
> > function [c,f,s] = pdex1pde(x,t,u,DuDx)
> > c = [1 0; 0 1];
> > f = [0 0; 1 0] * DuDx;
> > s = [u(2); 0];
> >
> > %
> >
> ------------------------------------------------------
>
> > --------
> > function u0 = pdex1ic(x)
> > u0 = [0; 1];
> > %
>
> Set u0(2) to 0 if x equals 1.

Correction : Set u0(2) to 0 if x equals 0 or 1.

> Otherwise initial conditions and boundary conditions
> are not consistent (which often causes the error
> from
> below).
>
>
> >
> ------------------------------------------------------
>
> > --------
> > function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t)
> > pl = [ul(1); ul(2)];
> > ql = [0; 0];
> > pr = [ur(1); ur(2)];
> > qr = [0; 0];
> >
> //////////////////////////////////////////////////////
>
> > ////////////////////
> >
> > But have error:
> >
> > ??? Error using ==> daeic12 at 77
> > This DAE appears to be of index greater than 1.
> >
> > Help me. Thank a lot.
>
>
> Best wishes
> Torsten.
From: trung trinh on 12 Apr 2010 08:15
hi helper, boundary is not important, if i change boundary and make it more complex, i can't solve this problem. i can try that and check.
Thank for your answer
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