After a call to nag_ode_ivp_rk_range (d02pc) or nag_ode_ivp_rk_onestep (d02pd), nag_ode_ivp_rk_diag (d02py) can be called to obtain information about the cost of the integration and the size of the next step.

References

Brankin R W, Gladwell I and Shampine L F (1991) RKSUITE: A suite of Runge–Kutta codes for the initial value problems for ODEs SoftReport 91-S1 Southern Methodist University

Parameters

Compulsory Input Parameters

None.

Optional Input Parameters

None.

Output Parameters

1: $totfcn$ – int64int32nag_int scalar: The total number of evaluations of $f$ used in the primary integration so far; this includes evaluations of $f$ for the secondary integration specified by a prior call to nag_ode_ivp_rk_setup (d02pv) with $errass = true$ .
2: $stpcst$ – int64int32nag_int scalar: The cost in terms of number of evaluations of $f$ of a typical step with the method being used for the integration. The method is specified by the argument method in a prior call to nag_ode_ivp_rk_setup (d02pv).
3: $waste$ – double scalar: The number of attempted steps that failed to meet the local error requirement divided by the total number of steps attempted so far in the integration. A ‘large’ fraction indicates that the integrator is having trouble with the problem being solved. This can happen when the problem is ‘stiff’ and also when the solution has discontinuities in a low-order derivative.
4: $stpsok$ – int64int32nag_int scalar: The number of accepted steps.
5: $hnext$ – double scalar: The step size the integrator will attempt to use for the next step.
6: $ifail$ – 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:

$ifail = 1$: An invalid call to nag_ode_ivp_rk_diag (d02py) has been made, for example without a previous call to nag_ode_ivp_rk_range (d02pc) or nag_ode_ivp_rk_onestep (d02pd). You cannot continue integrating the problem.

$ifail = - 99$: 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

When a secondary integration has taken place, that is when global error assessment has been specified using

errass = true

in a prior call to nag_ode_ivp_rk_setup (d02pv), then the approximate extra number of evaluations of

f

used is given by

2 \times stpsok \times stpcst

for

method = 2

3

and

3 \times stpsok \times stpcst

for

method = 1

Example

See Example in nag_ode_ivp_rk_range (d02pc), nag_ode_ivp_rk_onestep (d02pd), nag_ode_ivp_rk_reset_tend (d02pw), nag_ode_ivp_rk_interp (d02px) and nag_ode_ivp_rk_errass (d02pz).

Open in the MATLAB editor: d02py_example

function d02py_example


fprintf('d02py example results\n\n');

tstart = 0;
ystart = [0; 1];
tend = 6.283185307179586;
tol = 0.001;
thres = [1e-08; 1e-08];
method = int64(2);
task = 'Complex Task';
errass = false;
lenwrk = int64(64);
neq = int64(2);
twant = 0.3926990816987241;
reqest = 'Both';
nwant = int64(1);
wrkint = zeros(7, 1);
[work, ifail] = ...
    d02pv(tstart, ystart, tend, tol, thres, method, task, errass, lenwrk);
npts = 16;
tnow = tend-1;
while (tnow < tend)
  [tnow, ynow, ypnow, work, ifail] = d02pd(@f, neq, work);
  j = npts -1;
  tinc = tend/npts;
  while (twant <= tnow)
    [ywant, ypwant, work, wrkint, ifail] = ...
    d02px(neq, twant, reqest, nwant, @f, work, wrkint);
    j = j-1;
    twant = tend -j*tinc;
  end
end
[totfcn, stpcst, waste, stpsok, hnext, ifail] = d02py



function [yp] = f(t, y)
% Evaluate derivative vector.
yp = zeros(2, 1);
yp(1) =  y(2);
yp(2) = -y(1);

d02py example results


totfcn =

                   68


stpcst =

                    7


waste =

    0.1429


stpsok =

                    6


hnext =

    1.4387


ifail =

                    0

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