NAG Toolbox: nag_ode_ivp_rkts_errass (d02pu)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

$n$, the number of ordinary differential equations in the system to be solved by the integration function.

Constraint: $\mathbf{n}\ge 1$.

2:     $\mathrm{iwsav}\left(130\right)$ – int64int32nag_int array

3:     $\mathrm{rwsav}\left(32\times \mathbf{n}+350\right)$ – double array

These must be the same arrays supplied in a previous call to nag_ode_ivp_rkts_range (d02pe) or nag_ode_ivp_rkts_onestep (d02pf). They must remain unchanged between calls.

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{rmserr}\left(\mathbf{n}\right)$ – double array

$\mathbf{rmserr}\left(\mathit{i}\right)$ approximates the RMS average of the true error of the numerical solution for the $\mathit{i}$th solution component, for $\mathit{i}=1,2,\dots ,\mathit{n}$. The average is taken over all steps from the beginning of the integration to the current integration point.

2:     $\mathrm{errmax}$ – double scalar

The maximum weighted approximate true error taken over all solution components and all steps.

3:     $\mathrm{terrmx}$ – double scalar

The first value of the independent variable where an approximate true error attains the maximum value, errmax.

4:     $\mathrm{iwsav}\left(130\right)$ – int64int32nag_int array

5:     $\mathrm{rwsav}\left(32\times \mathbf{n}+350\right)$ – double array

Information about the integration for use on subsequent calls to nag_ode_ivp_rkts_range (d02pe) or nag_ode_ivp_rkts_onestep (d02pf) or other associated functions.

6:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

No error assessment is available since the integrator has not actually taken any successful steps.

No error assessment is available since you did not ask for it in your call to the setup function.

On entry, a previous call to the setup function has not been made or the communication arrays have become corrupted, or a catastrophic error has already been detected elsewhere.
You cannot continue integrating the problem.

On entry, $\mathbf{n}=\_$, but the value passed to the setup function was .

You cannot call this function before you have called the integrator.

You have already made one call to this function after the integrator could not achieve specified accuracy.
You cannot call this function again.

   $\mathbf{ifail}=-99$

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

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: d02pu_example

function d02pu_example


fprintf('d02pu example results\n\n');

% Set initial conditions and input
n      = int64(4);
method = int64(3);
tstart = 0;
tend   = 3*pi;
ecc    = 0.7;
yinit  = [1-ecc; 0; 0; sqrt((1+ecc)/(1-ecc))];
hstart = 0;
thresh = [1e-10; 1e-10; 1e-10; 1e-10];
npts   = 96;
ygot   = zeros(n, 1);
ymax   = zeros(n, 1);


% Set control for output
tol    = 1e-6;
tinc   = (tend-tstart)/npts;



% Call setup function
[iwsav, rwsav, ifail] = d02pq( ...
                              tstart, tend, yinit, tol, thresh, method);

fprintf('\nCalculation with TOL = %8.1e\n\n', tol);
fprintf('    t         y1         y2         y3         y4\n');
fprintf(' %6.3f   %8.4f   %8.4f   %8.4f   %8.4f\n', tstart, yinit);

twant = tend;

ifail = int64(3);
while ifail == 2 || ifail == 3 || ifail == 4
  [tgot, ygot, ypgot, ymax, user, iwsav, rwsav, ifail] = ...
    d02pe(@f, twant, ygot, ymax, iwsav, rwsav);
end


% Print Solution
fprintf(' %6.3f   %8.4f   %8.4f   %8.4f   %8.4f\n', tgot, ygot);

% Compute and print error estimates.
[rmserr, errmax, terrmx, iwsav, rwsav, ifail] = d02pu(n, iwsav, rwsav);

fprintf('\nComponentwise error assessment\n');
fprintf('%9.2e ', rmserr);
fprintf('\nMaximum global error, at t = %6.3f, was %9.2e\n', terrmx, errmax);

[fevals, stepcost, waste, stepsok, hnext, iwsav, ifail] = ...
    d02pt(iwsav, rwsav);
fprintf('\nCost of the integration in evaluations of f is %d\n', fevals);



function [yp, user] = f(t, n, y, user)
  r = sqrt(y(1)^2+y(2)^2);
  yp = [y(3); y(4); -y(1)/r^3; -y(2)/r^3];

d02pu example results


Calculation with TOL =  1.0e-06

    t         y1         y2         y3         y4
  0.000     0.3000     0.0000     0.0000     2.3805
  9.425    -1.7000     0.0000    -0.0000    -0.4201

Componentwise error assessment
 3.81e-06  7.10e-06  6.92e-06  2.10e-06 
Maximum global error, at t =  6.302, was  3.43e-05

Cost of the integration in evaluations of f is 1361