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See the recommended documentation of this function

# impl

differential algebraic equation

### Arguments

y0, ydot0

real vectors or matrices (initial conditions)

t0

a real scalar (initial time)

t

a real vector (times at which the solution is computed)

externals (function or character string or list)

type

atol, rtol

real scalars or real vectors of the same size as y

jac

external (function or character string or list).

### Description

Solution of the linear implicit differential equation

A(t,y) dy/dt=g(t,y), y(t0)=y0

t0 is the initial instant, y0 is the vector of initial conditions. Vector ydot0 of the time derivative of y at t0 must also be given. The input res is an external i.e. a function with specified syntax, or the name a Fortran subroutine or a C function (character string) with specified calling sequence or a list.

If res is a function, its syntax must be as follows:

r = res(t,y,ydot)

where t is a real scalar (time) and y and ydot are real vector (state and derivative of the state). This function must return r=g(t,y)-A(t,y)*ydot.

If res is a character string, it refers to the name of a Fortran subroutine or a C function. See SCI/modules/differential_equations/sci_gateway/fortran/Ex-impl.f for an example to do that.

res can also be a list: see the help of ode.

The input adda is also an external.

If adda is a function, its syntax must be as follows:

and it must return r=A(t,y)+p where p is a matrix to be added to A(t,y).

If adda is a character string, it refers to the name of a Fortran subroutine or a C function. See SCI/modules/differential_equations/sci_gateway/fortran/Ex-impl.f for an example to do that.

adda can also be a list: see the help of ode.

The input jac is also an external.

If jac is a function, its syntax must be as follows:

j = jac(t,y,ydot)

and it must return the Jacobian of r=g(t,y)-A(t,y)*ydot with respect to y.

If jac is a character string, it refers to the name of a Fortran subroutine or a C function. See SCI/modules/differential_equations/sci_gateway/fortran/Ex-impl.f for an example to do that.

jac can also be a list: see the help of ode.

### Examples

y=impl([1;0;0],[-0.04;0.04;0],0,0.4,'resid','aplusp');
// Using hot restart
//[x1,w,iw]=impl([1;0;0],[-0.04;0.04;0],0,0.2,'resid','aplusp');
// hot start from previous call
//[x1]=impl([1;0;0],[-0.04;0.04;0],0.2,0.4,'resid','aplusp',w,iw);
//max(abs(x1-x))

• dassl — differential algebraic equation
• ode — solveur d'équations différentielles ordinaires
• external — Objet Scilab, fonction externe ou routine