# [petsc-dev] [petsc-maint #58517] re: TS for DAEs

Barry Smith bsmith at mcs.anl.gov
Wed Dec 15 11:22:00 CST 2010

```On Dec 15, 2010, at 8:59 AM, Michael E Henderson wrote:

> Somehow it seems like as soon as I ask a question I figure it out myself.
>
> My initial solution does not satisfy the algebraic constraint!
>
> Looks like TSTheta is solving
>
>               F( (u_1-u_0)/dt,(u_1+u_0)/2,t)=0.
>
> which makes sense. My algebraic constraint is something like u[0]-Ttop=0.
> For that component the above equation is
>
>              (u_1[0]+u_0[0])/2-Ttop=0            or u_1[0] = 2Ttop -
> u_0[0]
>
> so (u_1-u_0)/dt = 2(Ttop-u_0[0])/dt. If dt is small this derivative is
> large if u_0[0] != Ttop.
>
> Thanks anyway,
>
> Mike Henderson
> ------------------------------------------------------------------------------------------------------------------------------------
> Mathematical Sciences, TJ Watson Research Center
> mhender at watson.ibm.com
> http://www.research.ibm.com/people/h/henderson/
> http://multifario.sourceforge.net/
>
> Somehow it seems like as soon as I ask a question I figure it out myself.
>
> My initial solution does not satisfy the algebraic constraint!
>
> Looks like TSTheta is solving
>
>                F( (u_1-u_0)/dt,(u_1+u_0)/2,t)=0.
>
> which makes sense. My algebraic constraint is something like u[0]-Ttop=0. For that component the above equation is
>
>               (u_1[0]+u_0[0])/2-Ttop=0            or u_1[0] = 2Ttop - u_0[0]
>
> so (u_1-u_0)/dt = 2(Ttop-u_0[0])/dt. If dt is small this derivative is large if u_0[0] != Ttop.
>
> Thanks anyway,
>
> Mike Henderson
> ------------------------------------------------------------------------------------------------------------------------------------
> Mathematical Sciences, TJ Watson Research Center
> mhender at watson.ibm.com
> http://www.research.ibm.com/people/h/henderson/
> http://multifario.sourceforge.net/

```