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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_ode_ivp_stiff_contin (d02nz)

▸▿ Contents

    1  Purpose
    2  Syntax
    3  Description
    4  References
▸▿ 5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

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:     neqmax – int64int32nag_int scalar
The value used for the argument neqmax when calling the integrator.
Constraint: neqmax≥1.
2:     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:     h – double scalar
The next step size to be attempted. Set h=0.0 if the current value of h is not to be changed.
4:     hmin – double scalar
The minimum absolute step size to be allowed. Set hmin=0.0 if this option is not required. Set hmin<0.0 if the current value of hmin is not to be changed.
5:     hmax – double scalar
The maximum absolute step size to be allowed. Set hmax=0.0 if this option is not required. Set hmax<0.0 if the current value of hmax is not to be changed.
6:     maxstp – int64int32nag_int scalar
The maximum number of steps to be attempted during one call to the integrator after which it will return with ifail=2 (see nag_ode_ivp_stiff_exp_bandjac (d02nc)). Set maxstp=0 if this option is not required. Set maxstp<0 if the current value of maxstp is not to be changed.
7:     mxhnil – int64int32nag_int scalar
The maximum number of warnings printed (if itrace≥0, e.g., see nag_ode_ivp_stiff_exp_fulljac (d02nb)) per problem when t+h=t on a step (h=​ current step size). If mxhnil≤0, a default value of 10 is assumed.
8:     rwork50+4×neqmax – 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).

Optional Input Parameters

None.

Output Parameters

1:     rwork50+4×neqmax – double array
2:     ifail – int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
   ifail=1
neqmax<1.
   ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
   ifail=-399
Your licence key may have expired or may not have been installed correctly.
   ifail=-999
Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

None.

Example

See Example in nag_ode_ivp_stiff_exp_bandjac (d02nc).

Open in the MATLAB editor: d02nz_example

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');
itask  = int64(1);
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, ...
          wkjac, jacpvt, 'd02nby', itask, itrace);

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, ...
          wkjac, jacpvt, 'd02nby', itask, itrace);

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
PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox
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