Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_ode_ivp_stiff_contin (d02nz)

Purpose

nag_ode_ivp_stiff_contin (d02nz) is a setup function which must be called, if optional inputs need resetting, prior to a continuation call to any of those integrators in Sub-chapter D02M–N that use methods set up by calls to nag_ode_ivp_stiff_dassl (d02mv), nag_ode_ivp_stiff_bdf (d02nv) or nag_ode_ivp_stiff_blend (d02nw).

Syntax

[rwork, ifail] = d02nz(neqmax, tcrit, h, hmin, hmax, maxstp, mxhnil, rwork)
[rwork, ifail] = nag_ode_ivp_stiff_contin(neqmax, tcrit, h, hmin, hmax, maxstp, mxhnil, rwork)

Description

nag_ode_ivp_stiff_contin (d02nz) is provided to permit you to reset many of the arguments which control the integration ‘on the fly’, that is in conjunction with the interrupt facility permitted through the argument itask of the integrator (e.g., see nag_ode_ivp_stiff_exp_fulljac (d02nb)). In addition to a number of arguments which you can set initially through one of the integrator setup functions, the step size to be attempted on the next step may be changed.

References

See the D02M–N Sub-chapter Introduction.

Parameters

Compulsory Input Parameters

1:     $\mathrm{neqmax}$int64int32nag_int scalar
The value used for the argument neqmax when calling the integrator.
Constraint: ${\mathbf{neqmax}}\ge 1$.
2:     $\mathrm{tcrit}$ – double scalar
A point beyond which integration must not be attempted. The use of tcrit is described under the argument itask in the specification for the integrator (e.g., see nag_ode_ivp_stiff_exp_fulljac (d02nb)). A value, $0.0$ say, must be specified even if itask subsequently specifies that tcrit will not be used.
3:     $\mathrm{h}$ – double scalar
The next step size to be attempted. Set ${\mathbf{h}}=0.0$ if the current value of h is not to be changed.
4:     $\mathrm{hmin}$ – double scalar
The minimum absolute step size to be allowed. Set ${\mathbf{hmin}}=0.0$ if this option is not required. Set ${\mathbf{hmin}}<0.0$ if the current value of hmin is not to be changed.
5:     $\mathrm{hmax}$ – double scalar
The maximum absolute step size to be allowed. Set ${\mathbf{hmax}}=0.0$ if this option is not required. Set ${\mathbf{hmax}}<0.0$ if the current value of hmax is not to be changed.
6:     $\mathrm{maxstp}$int64int32nag_int scalar
The maximum number of steps to be attempted during one call to the integrator after which it will return with ${\mathbf{ifail}}={\mathbf{2}}$ (see nag_ode_ivp_stiff_exp_bandjac (d02nc)). Set ${\mathbf{maxstp}}=0$ if this option is not required. Set ${\mathbf{maxstp}}<0$ if the current value of maxstp is not to be changed.
7:     $\mathrm{mxhnil}$int64int32nag_int scalar
The maximum number of warnings printed (if ${\mathbf{itrace}}\ge 0$, e.g., see nag_ode_ivp_stiff_exp_fulljac (d02nb)) per problem when $t+h=t$ on a step ($h=\text{​ current step size}$). If ${\mathbf{mxhnil}}\le 0$, a default value of $10$ is assumed.
8:     $\mathrm{rwork}\left(50+4×{\mathbf{neqmax}}\right)$ – double array
This must be the same workspace array as the array rwork supplied to the integrator. It is used to pass information from the integrator to nag_ode_ivp_stiff_contin (d02nz) and therefore its contents must not be changed before calling nag_ode_ivp_stiff_contin (d02nz).

None.

Output Parameters

1:     $\mathrm{rwork}\left(50+4×{\mathbf{neqmax}}\right)$ – double array
2:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
${\mathbf{neqmax}}<1$.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

Not applicable.

None.

Example

See Example in nag_ode_ivp_stiff_exp_bandjac (d02nc).
```function d02nz_example

fprintf('d02nz example results\n\n');

% Initialize variables and arrays for setup routine
n      = int64(3);
ord    = int64(11);
sdy    = int64(ord + 3);
petzld = false;
con    = zeros(6);
tcrit  = 0;
hmin   = 1.0e-10;
hmax   = 10;
h0     = 0;
maxstp = int64(200);
mxhnil = int64(5);
lrwork = 50 + 4*n;
rwork  = zeros(lrwork);
[const, rwork, ifail] = d02nw(n, sdy, ord, con, tcrit, hmin, hmax, h0, ...
maxstp, mxhnil, 'Average-L2', rwork);

% Setup for banded Jacbian using d02nt
ml     = int64(1);
mu     = int64(2);
nwkjac = int64(15);
[rwork, ifail] = d02nt(n, n, 'Analytical', ml, mu, nwkjac, n, rwork);

% Initialize variables and arrays for integration
t      = 0;
tout   = 5;
y      = [1; 0; 0];
rtol   = [0.0001];
atol   = [1e-07; 1e-08; 1e-07];
itol   = int64(2);
inform = zeros(23, 1, 'int64');
ysave  = zeros(n, sdy);
wkjac  = zeros(nwkjac, 1);
jacpvt = zeros(n, 1, 'int64');
itrace = int64(0);

% Integrate ODE from t=0 to t=tout, no monitoring, using d02nc
[t, y, ydot, rwork, inform, ysave, wkjac, jacpvt, ifail] = ...
d02nc(t, tout, y, rwork, rtol, atol, itol, inform, @fcn, ysave, @jac, ...

fprintf('Solution y and derivative y'' at t = %7.4f is:\n',t);
fprintf('\n %10s %10s\n','y','y''');
for i=1:n
fprintf(' %10.4f %10.4f\n',y(i),ydot(i));
end

% Call to d02nz to alow continuation of integration up to t=10.
[rwork, ifail] = d02nz(n, tcrit, h0, hmin, hmax, maxstp, mxhnil, rwork);

tout = 10;
% Integrate ODE from t to t=tout, no monitoring, using d02nc
[t, y, ydot, rwork, inform, ysave, wkjac, jacpvt, ifail] = ...
d02nc(t, tout, y, rwork, rtol, atol, itol, inform, @fcn, ysave, @jac, ...

fprintf('Solution y and derivative y'' at t = %7.4f is:\n',t);
fprintf('\n %10s %10s\n','y','y''');
for i=1:n
fprintf(' %10.4f %10.4f\n',y(i),ydot(i));
end

function [f, ires] = fcn(neq, t, y, ires)
% Evaluate derivative vector.
f = zeros(3,1);
f(1) = -0.04d0*y(1) + 1.0d4*y(2)*y(3);
f(2) =  0.04d0*y(1) - 1.0d4*y(2)*y(3) - 3.0d7*y(2)*y(2);
f(3) =                                  3.0d7*y(2)*y(2);

function p = jac(neq, t, y, h, d, ml, mu, pIn)
% Evaluate the Jacobian.
p = zeros(ml+mu+1, neq);
hxd = h*d;
p(1,1) = 1.0d0 - hxd*(-0.04d0);
p(2,1) = -hxd*(1.0d4*y(3));
p(3,1) = -hxd*(1.0d4*y(2));
p(1,2) = -hxd*(0.04d0);
p(2,2) = 1.0d0 - hxd*(-1.0d4*y(3)-6.0d7*y(2));
p(3,2) = -hxd*(-1.0d4*y(2));
p(1,3) = -hxd*(6.0d7*y(2));
p(2,3) = 1.0d0 - hxd*(0.0d0);
```
```d02nz example results

Solution y and derivative y' at t =  5.0000 is:

y         y'
0.8915    -0.0124
0.0000    -0.0000
0.1085     0.0124
Solution y and derivative y' at t = 10.0000 is:

y         y'
0.8414    -0.0078
0.0000    -0.0000
0.1586     0.0078
```

Chapter Contents
Chapter Introduction
NAG Toolbox

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2015