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dasrt
DAE solver with zero crossing
Calling Sequence
[r,nn,[,hd]]=dasrt(x0,t0,t [,atol,[rtol]],res [,jac],ng, surf [,info] [,hd])
Arguments
- x0
is either
y0
(ydot0
is estimated bydassl
with zero as first estimate) or the matrix[y0 ydot0]
.g(t,y0,ydot0)
must be equal to zero. If you only know an estimate ofydot0
setinfo(7)=1
- y0
real column vector of initial conditions.
- ydot0
real column vector of the time derivative of
y
att0
(may be an estimate).
- t0
real number is the initial instant.
- t
real scalar or vector. Gives instants for which you want the solution. Note that you can get solution at each dassl's step point by setting
info(2)=1
.- nn
a vector with two entries
[times num]
times
is the value of the time at which the surface is crossed,num
is the number of the crossed surface- atol,rtol
real scalars or column vectors of same size as
y
.atol,rtol
give respectively absolute and relative error tolerances of solution. If vectors the tolerances are specified for each component ofy
.- res
external (function or list or string). Computes the value of
g(t,y,ydot)
.It may be :A Scilab function.
Its calling sequence must be
[r,ires]=res(t,y,ydot)
andres
must return the residuer=g(t,y,ydot)
and error flagires
.ires = 0
ifres
succeeds to computer
,=-1
if residue is locally not defined for(t,y,ydot)
,=-2
if parameters are out of admissible range.A list.
This form allows to pass parameters other than t,y,ydot to the function. It must be as follows:
list(res,x1,x2,...)
where the calling sequence of the function
res
is nowr=res(t,y,ydot,x1,x2,...)
res
still returnsr=g(t,y,ydot)
as a function of(t,y,ydot,x1,x2,...)
.Warning: this form must not be used if there is no extra argument to pass to
the function.
A string.
it must refer to the name of a C or fortran subroutine linked with Scilab.
In C The calling sequence must be:
In Fortran it must be:
subroutine res(t,y,yd,r,ires,rpar,ipar) double precision t, y(*),yd(*),r(*),rpar(*) integer ires,ipar(*)
The rpar and ipar arrays must be present but cannot be used.
- jac
external (function or list or string). Computes the value of
dg/dy+cj*dg/dydot
for a given value of parametercj
A Scilab function.
Its calling sequence must be
r=jac(t,y,ydot,cj)
and thejac
function must returnr=dg(t,y,ydot)/dy+cj*dg(t,y,ydot)/dydot
wherecj
is a real scalarA list.
it must be as follows
list(jac,x1,x2,...)
where the calling sequence of the function
jac
is nowr=jac(t,y,ydot,cj,x1,x2,...)
jac
still returnsdg/dy+cj*dg/dydot
as a function of(t,y,ydot,cj,x1,x2,...)
.A character string.
it must refer to the name of a fortran subroutine linked with scilab
In C The calling sequence must be:
In Fortran it must be:
subroutine jac(t,y,yd,pd,cj,rpar,ipar) double precision t, y(*),yd(*),pd(*),cj,rpar(*) integer ipar(*)
- surf
external (function or list or string). Computes the value of the column vector
surf(t,y)
withng
components. Each component defines a surface. It may be defined by:A Scilab function.
Its calling sequence must be
surf(t,y)
A list.
it must be as follows
where the calling sequence of the function
surf
is nowr=surf(t,y,x1,x2,...)
A character string.
it must refer to the name of a fortran subroutine linked with scilab
In C The calling sequence must be:
In Fortran it must be:
- info
list which contains
7
elements, default value is list([],0,[],[],[],0,0)- info(1)
real scalar which gives the maximum time for which
g
is allowed to be evaluated or an empty matrix[]
if no limits imposed for time.- info(2)
flag which indicates if
dassl
returns its intermediate computed values (flag=1
) or only the user specified time point values (flag=0
).- info(3)
2
components vector which give the definition[ml,mu]
of band matrix computed byjac
;r(i - j + ml + mu + 1,j) = "dg(i)/dy(j)+cj*dg(i)/dydot(j)"
. Ifjac
returns a full matrix setinfo(3)=[]
.- info(4)
real scalar which gives the maximum step size. Set
info(4)=[]
if no limitation.- info(5)
real scalar which gives the initial step size. Set
info(4)=[]
if not specified.- info(6)
set
info(6)=1
if the solution is known to be non negative, else setinfo(6)=0
.- info(7)
set
info(7)=1
ifydot0
is just an estimation,info(7)=0
ifg(t0,y0,ydot0)=0
.
- hd
real vector which allows to store the
dassl
context and to resume integration- r
real matrix . Each column is the vector [t;x(t);xdot(t)] where t is time index for which the solution had been computed
Description
Solution of the implicit differential equation
g(t,y,ydot)=0 y(t0)=y0 and ydot(t0)=ydot0
Returns the surface crossing instants and the number of the surface
reached in nn
.
Detailed examples can be found in SCIDIR/tests/dassldasrt.tst
Examples
//dy/dt = ((2*log(y)+8)/t -5)*y, y(1) = 1, 1<=t<=6 //g1 = ((2*log(y)+8)/t - 5)*y //g2 = log(y) - 2.2491 y0=1;t=2:6;t0=1;y0d=3; atol=1.d-6;rtol=0;ng=2; deff('[delta,ires]=res1(t,y,ydot)','ires=0;delta=ydot-((2*log(y)+8)/t-5)*y') deff('[rts]=gr1(t,y)','rts=[((2*log(y)+8)/t-5)*y;log(y)-2.2491]') [yy,nn]=dasrt([y0,y0d],t0,t,atol,rtol,res1,ng,gr1); //(Should return nn=[2.4698972 2])
See Also
<< daeoptions | Equations Differentielles | dassl >> |