DAE solver with zero crossing (original) (raw)

Scilab 5.3.3

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Scilab help >> Differential Equations, Integration > dasrt

dasrt

DAE solver with zero crossing

Calling Sequence

[r,nn,[,hd]]=dasrt(x0,t0,t [,atol,[rtol]],res [,jac],ng, surf [,info] [,hd])

Arguments

is either y0 (ydot0 is estimated by dassl 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 of ydot0 setinfo(7)=1

real column vector of initial conditions.

ydot0

real column vector of the time derivative ofy at t0 (may be an estimate).

real number is the initial instant.

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.

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 asy. 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 ofg(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 compute r,=-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:
where the calling sequence of the functionres is now
r=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 ofdg/dy+cj*dg/dydot for a given value of parametercj

A Scilab function.
Its calling sequence must ber=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 scalar
A list.
it must be as follows
where the calling sequence of the functionjac is now
r=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 besurf(t,y)
A list.
it must be as follows
where the calling sequence of the functionsurf is now
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 surf(ny,t,y,ng,gout)
double precision t, y(),gout()
integer ny,ng

info

list which contains 7 elements, default value is list([],0,[],[],[],0,0)

info(1)

real scalar which gives the maximum time for whichg 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 by jac; 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. Setinfo(4)=[] if no limitation.

info(5)

real scalar which gives the initial step size. Setinfo(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.

real vector which allows to store the dassl context and to resume integration

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

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=[((2log(y)+8)/t-5)*y;log(y)-2.2491]')