D02PWF resets the end point in an integration performed by
D02PDF.
D02PWF and its associated routines (
D02PDF,
D02PVF,
D02PXF,
D02PYF and
D02PZF) solve the initial value problem for a first-order system of ordinary differential equations. The routines, based on Runge–Kutta methods and derived from RKSUITE (see
Brankin et al. (1991)), integrate
where
$y$ is the vector of
$n$ solution components and
$t$ is the independent variable.
D02PWF is used to reset the final value of the independent variable,
${t}_{f}$, when the integration is already underway. It can be used to extend or reduce the range of integration. The new value must be beyond the current value of the independent variable (as returned in
TNOW by
D02PDF) in the current direction of integration. It is much more efficient to use D02PWF for this purpose than to use
D02PVF which involves the overhead of a complete restart of the integration.
If you want to change the direction of integration then you must restart by a call to
D02PVF.
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
If on entry
${\mathbf{IFAIL}}={\mathbf{0}}$ or
${-{\mathbf{1}}}$, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Not applicable.
None.
This example integrates a two body problem. The equations for the coordinates
$\left(x\left(t\right),y\left(t\right)\right)$ of one body as functions of time
$t$ in a suitable frame of reference are
The initial conditions
lead to elliptic motion with
$0<\epsilon <1$.
$\epsilon =0.7$ is selected and reposed as
over the range
$\left[0,6\pi \right]$. Relative error control is used with threshold values of
$\text{1.0E\u221210}$ for each solution component and compute the solution at intervals of length
$\pi $ across the range using D02PWF to reset the end of the integration range. A high-order Runge–Kutta method (
${\mathbf{METHOD}}=3$) is also used with tolerances
${\mathbf{TOL}}=\text{1.0E\u22124}$ and
${\mathbf{TOL}}=\text{1.0E\u22125}$ in turn so that the solutions may be compared. The value of
$\pi $ is obtained by using
X01AAF.
Note that the length of
${\mathbf{TOL}}=\text{1.0E\u22124}$ and
WORK is large enough for any valid combination of input arguments to
D02PVF.