NAG Library Routine Document

d02tlf  (bvp_coll_nlin_solve)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{ffun}$ – Subroutine, supplied by the user.External Procedure

ffun must evaluate the functions $f_i$ for given values $x,z\left(y\left(x\right)\right)$.

The specification of ffun is:

Fortran Interface

Subroutine ffun ( x, y, neq, m, f, iuser, ruser) Integer, Intent (In) :: neq, m(neq) Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: x, y(neq,$0:*$) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (Out) :: f(neq)

C Header Interface

#include nagmk26.h void  ffun ( const double *x, const double y[], const Integer *neq, const Integer m[], double f[], Integer iuser[], double ruser[])

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: $x$, the independent variable.

2:     $\mathbf{y}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{y}\left(\mathit{i},\mathit{j}\right)$ contains $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(x\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(x\right)=y_i\left(x\right)$.

3:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

4:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

5:     $\mathbf{f}\left(\mathbf{neq}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{f}\left(\mathit{i}\right)$ must contain $f_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

ffun is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to ffun.

ffun must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: ffun should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

2:     $\mathbf{fjac}$ – Subroutine, supplied by the user.External Procedure

fjac must evaluate the partial derivatives of $f_i$ with respect to the elements of
$z\left(y\left(x\right)\right)=\left(y_1\left(x\right),y_1^1\left(x\right),\dots ,y_1^{\left(m_1-1\right)}\left(x\right),y_2\left(x\right),\dots ,y_n^{\left(m_n-1\right)}\left(x\right)\right)$.

The specification of fjac is:

Fortran Interface

Subroutine fjac ( x, y, neq, m, dfdy, iuser, ruser) Integer, Intent (In) :: neq, m(neq) Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: x, y(neq,$0:*$) Real (Kind=nag_wp), Intent (Inout) :: dfdy(neq,neq,$0:*$), ruser(*)

C Header Interface

#include nagmk26.h void  fjac ( const double *x, const double y[], const Integer *neq, const Integer m[], double dfdy[], Integer iuser[], double ruser[])

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: $x$, the independent variable.

2:     $\mathbf{y}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{y}\left(\mathit{i},\mathit{j}\right)$ contains $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(x\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(x\right)=y_i\left(x\right)$.

3:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

4:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

5:     $\mathbf{dfdy}\left(\mathbf{neq},\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: set to zero.

On exit: $\mathbf{dfdy}\left(\mathit{i},\mathit{j},\mathit{k}\right)$ must contain the partial derivative of $f_{\mathit{i}}$ with respect to $y_{\mathit{j}}^{\left(\mathit{k}\right)}$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$, $\mathit{j}=1,2,\dots ,\mathbf{neq}$ and $\mathit{k}=0,1,\dots ,\mathbf{m}\left(\mathit{j}\right)-1$. Only nonzero partial derivatives need be set.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

fjac is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to fjac.

fjac must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: fjac should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

3:     $\mathbf{gafun}$ – Subroutine, supplied by the user.External Procedure

gafun must evaluate the boundary conditions at the left-hand end of the range, that is functions $g_i\left(z\left(y\left(a\right)\right)\right)$ for given values of $z\left(y\left(a\right)\right)$.

The specification of gafun is:

Fortran Interface

Subroutine gafun ( ya, neq, m, nlbc, ga, iuser, ruser) Integer, Intent (In) :: neq, m(neq), nlbc Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: ya(neq,$0:*$) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (Out) :: ga(nlbc)

C Header Interface

#include nagmk26.h void  gafun ( const double ya[], const Integer *neq, const Integer m[], const Integer *nlbc, double ga[], Integer iuser[], double ruser[])

1:     $\mathbf{ya}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{ya}\left(\mathit{i},\mathit{j}\right)$ contains $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(a\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(a\right)=y_i\left(a\right)$.

2:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

3:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

4:     $\mathbf{nlbc}$ – IntegerInput

On entry: the number of boundary conditions at $a$.

5:     $\mathbf{ga}\left(\mathbf{nlbc}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{ga}\left(\mathit{i}\right)$ must contain $g_{\mathit{i}}\left(z\left(y\left(a\right)\right)\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nlbc}$.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

gafun is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to gafun.

gafun must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: gafun should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

4:     $\mathbf{gbfun}$ – Subroutine, supplied by the user.External Procedure

gbfun must evaluate the boundary conditions at the right-hand end of the range, that is functions ${\stackrel{-}{g}}_i\left(z\left(y\left(b\right)\right)\right)$ for given values of $z\left(y\left(b\right)\right)$.

The specification of gbfun is:

Fortran Interface

Subroutine gbfun ( yb, neq, m, nrbc, gb, iuser, ruser) Integer, Intent (In) :: neq, m(neq), nrbc Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: yb(neq,$0:*$) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (Out) :: gb(nrbc)

C Header Interface

#include nagmk26.h void  gbfun ( const double yb[], const Integer *neq, const Integer m[], const Integer *nrbc, double gb[], Integer iuser[], double ruser[])

1:     $\mathbf{yb}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{yb}\left(\mathit{i},\mathit{j}\right)$ contains $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(b\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(b\right)=y_i\left(b\right)$.

2:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

3:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

4:     $\mathbf{nrbc}$ – IntegerInput

On entry: the number of boundary conditions at $b$.

5:     $\mathbf{gb}\left(\mathbf{nrbc}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{gb}\left(\mathit{i}\right)$ must contain ${\stackrel{-}{g}}_{\mathit{i}}\left(z\left(y\left(b\right)\right)\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nrbc}$.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

gbfun is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to gbfun.

gbfun must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: gbfun should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

5:     $\mathbf{gajac}$ – Subroutine, supplied by the user.External Procedure

gajac must evaluate the partial derivatives of $g_i\left(z\left(y\left(a\right)\right)\right)$ with respect to the elements of $z\left(y\left(a\right)\right)=\left(y_1\left(a\right),y_1^1\left(a\right),\dots ,y_1^{\left(m_1-1\right)}\left(a\right),y_2\left(a\right),\dots ,y_n^{\left(m_n-1\right)}\left(a\right)\right)$.

The specification of gajac is:

Fortran Interface

Subroutine gajac ( ya, neq, m, nlbc, dgady, iuser, ruser) Integer, Intent (In) :: neq, m(neq), nlbc Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: ya(neq,$0:*$) Real (Kind=nag_wp), Intent (Inout) :: dgady(nlbc,neq,$0:*$), ruser(*)

C Header Interface

#include nagmk26.h void  gajac ( const double ya[], const Integer *neq, const Integer m[], const Integer *nlbc, double dgady[], Integer iuser[], double ruser[])

1:     $\mathbf{ya}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{ya}\left(\mathit{i},\mathit{j}\right)$ contains $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(a\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(a\right)=y_i\left(a\right)$.

2:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

3:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

4:     $\mathbf{nlbc}$ – IntegerInput

On entry: the number of boundary conditions at $a$.

5:     $\mathbf{dgady}\left(\mathbf{nlbc},\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: set to zero.

On exit: $\mathbf{dgady}\left(\mathit{i},\mathit{j},\mathit{k}\right)$ must contain the partial derivative of $g_{\mathit{i}}\left(z\left(y\left(a\right)\right)\right)$ with respect to $y_{\mathit{j}}^{\left(\mathit{k}\right)}\left(a\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nlbc}$, $\mathit{j}=1,2,\dots ,\mathbf{neq}$ and $\mathit{k}=0,1,\dots ,\mathbf{m}\left(\mathit{j}\right)-1$. Only nonzero partial derivatives need be set.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

gajac is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to gajac.

gajac must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: gajac should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

6:     $\mathbf{gbjac}$ – Subroutine, supplied by the user.External Procedure

gbjac must evaluate the partial derivatives of ${\stackrel{-}{g}}_i\left(z\left(y\left(b\right)\right)\right)$ with respect to the elements of $z\left(y\left(b\right)\right)=\left(y_1\left(b\right),y_1^1\left(b\right),\dots ,y_1^{\left(m_1-1\right)}\left(b\right),y_2\left(b\right),\dots ,y_n^{\left(m_n-1\right)}\left(b\right)\right)$.

The specification of gbjac is:

Fortran Interface

Subroutine gbjac ( yb, neq, m, nrbc, dgbdy, iuser, ruser) Integer, Intent (In) :: neq, m(neq), nrbc Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: yb(neq,$0:*$) Real (Kind=nag_wp), Intent (Inout) :: dgbdy(nrbc,neq,$0:*$), ruser(*)

C Header Interface

#include nagmk26.h void  gbjac ( const double yb[], const Integer *neq, const Integer m[], const Integer *nrbc, double dgbdy[], Integer iuser[], double ruser[])

1:     $\mathbf{yb}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{yb}\left(\mathit{i},\mathit{j}\right)$ contains $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(b\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(b\right)=y_i\left(b\right)$.

2:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

3:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

4:     $\mathbf{nrbc}$ – IntegerInput

On entry: the number of boundary conditions at $b$.

5:     $\mathbf{dgbdy}\left(\mathbf{nrbc},\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: set to zero.

On exit: $\mathbf{dgbdy}\left(\mathit{i},\mathit{j},\mathit{k}\right)$ must contain the partial derivative of ${\stackrel{-}{g}}_{\mathit{i}}\left(z\left(y\left(b\right)\right)\right)$ with respect to $y_{\mathit{j}}^{\left(\mathit{k}\right)}\left(b\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nrbc}$, $\mathit{j}=1,2,\dots ,\mathbf{neq}$ and $\mathit{k}=0,1,\dots ,\mathbf{m}\left(\mathit{j}\right)-1$. Only nonzero partial derivatives need be set.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

gbjac is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to gbjac.

gbjac must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: gbjac should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

7:     $\mathbf{guess}$ – Subroutine, supplied by the user.External Procedure

guess must return initial approximations for the solution components $y_{\mathit{i}}^{\left(\mathit{j}\right)}$ and the derivatives $y_{\mathit{i}}^{\left(m_{\mathit{i}}\right)}$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$. Try to compute each derivative $y_i^{\left(m_i\right)}$ such that it corresponds to your approximations to $y_i^{\left(\mathit{j}\right)}$, for $\mathit{j}=0,1,\dots ,\mathbf{m}\left(i\right)-1$. You should not call ffun to compute $y_i^{\left(m_i\right)}$.

If d02tlf is being used in conjunction with d02txf as part of a continuation process, guess is not called by d02tlf after the call to d02txf.

The specification of guess is:

Fortran Interface

Subroutine guess ( x, neq, m, y, dym, iuser, ruser) Integer, Intent (In) :: neq, m(neq) Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: x Real (Kind=nag_wp), Intent (Inout) :: y(neq,$0:*$), ruser(*) Real (Kind=nag_wp), Intent (Out) :: dym(neq)

C Header Interface

#include nagmk26.h void  guess ( const double *x, const Integer *neq, const Integer m[], double y[], double dym[], Integer iuser[], double ruser[])

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: $x$, the independent variable; $x\in \left[a,b\right]$.

2:     $\mathbf{neq}$ – IntegerInput

On entry: the number of differential equations.

3:     $\mathbf{m}\left(\mathbf{neq}\right)$ – Integer arrayInput

On entry: $\mathbf{m}\left(\mathit{i}\right)$ contains $m_{\mathit{i}}$, the order of the $\mathit{i}$th differential equation, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

4:     $\mathbf{y}\left(\mathbf{neq},0:*\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{y}\left(\mathit{i},\mathit{j}\right)$ must contain $y_{\mathit{i}}^{\left(\mathit{j}\right)}\left(x\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$ and $\mathit{j}=0,1,\dots ,\mathbf{m}\left(\mathit{i}\right)-1$.
Note:  $y_i^{\left(0\right)}\left(x\right)=y_i\left(x\right)$.

5:     $\mathbf{dym}\left(\mathbf{neq}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{dym}\left(\mathit{i}\right)$ must contain $y_{\mathit{i}}^{\left(m_{\mathit{i}}\right)}\left(x\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{neq}$.

6:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

7:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

guess is called with the arguments iuser and ruser as supplied to d02tlf. You should use the arrays iuser and ruser to supply information to guess.

guess must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02tlf is called. Arguments denoted as Input must not be changed by this procedure.

Note: guess should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02tlf. If your code inadvertently does return any NaNs or infinities, d02tlf is likely to produce unexpected results.

8:     $\mathbf{rcomm}\left(*\right)$ – Real (Kind=nag_wp) arrayCommunication Array

Note: the dimension of this array is dictated by the requirements of associated functions that must have been previously called. This array must be the same array passed as argument rcomm in the previous call to d02tvf.

On entry: this must be the same array as supplied to d02tvf and must remain unchanged between calls.

On exit: contains information about the solution for use on subsequent calls to associated routines.

9:     $\mathbf{icomm}\left(*\right)$ – Integer arrayCommunication Array

Note: the dimension of this array is dictated by the requirements of associated functions that must have been previously called. This array must be the same array passed as argument icomm in the previous call to d02tvf.

On entry: this must be the same array as supplied to d02tvf and must remain unchanged between calls.

On exit: contains information about the solution for use on subsequent calls to associated routines.

10:   $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

11:   $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

iuser and ruser are not used by d02tlf, but are passed directly to ffun, fjac, gafun, gbfun, gajac, gbjac and guess and may be used to pass information to these routines.

12:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, because for this routine the values of the output arguments may be useful even if $\mathbf{ifail}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

Either the setup routine has not been called or the communication arrays have become corrupted. No solution will be computed.

$\mathbf{ifail}=2$

Numerical singularity has been detected in the Jacobian used in the Newton iteration.
No results have been generated. Check the coding of the routines for calculating the Jacobians of system and boundary conditions.

$\mathbf{ifail}=3$

All Newton iterations that have been attempted have failed to converge.
No results have been generated. Check the coding of the routines for calculating the Jacobians of system and boundary conditions.
Try to provide a better initial solution approximation.

$\mathbf{ifail}=4$

A Newton iteration has failed to converge. The computation has not succeeded but results have been returned for an intermediate mesh on which convergence was achieved.
These results should be treated with extreme caution.

$\mathbf{ifail}=5$

The expected number of sub-intervals required to continue the computation exceeds the maximum specified: $〈\mathit{\text{value}}〉$.
Results have been generated which may be useful.
Try increasing this number or relaxing the error requirements.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d02tlfe.f90)

10.2

Program Data

Program Data (d02tlfe.d)

10.3

Program Results

Program Results (d02tlfe.r)