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Subject: [Boost-commit] svn:boost r61440 - in sandbox/odeint/libs/numeric/odeint/doc: . html
From: mario.mulansky_at_[hidden]
Date: 2010-04-20 17:48:30
Author: mariomulansky
Date: 2010-04-20 17:48:28 EDT (Tue, 20 Apr 2010)
New Revision: 61440
URL: http://svn.boost.org/trac/boost/changeset/61440
Log:
doc...
Text files modified:
sandbox/odeint/libs/numeric/odeint/doc/html/index.html | 2
sandbox/odeint/libs/numeric/odeint/doc/steppers.qbk | 49 ++++++++++++++++++++++-----------------
2 files changed, 28 insertions(+), 23 deletions(-)
Modified: sandbox/odeint/libs/numeric/odeint/doc/html/index.html
==============================================================================
--- sandbox/odeint/libs/numeric/odeint/doc/html/index.html (original)
+++ sandbox/odeint/libs/numeric/odeint/doc/html/index.html 2010-04-20 17:48:28 EDT (Tue, 20 Apr 2010)
@@ -256,7 +256,7 @@
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: April 19, 2010 at 19:48:59 GMT</small></p></td>
+<td align="left"><p><small>Last revised: April 20, 2010 at 18:00:35 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>
Modified: sandbox/odeint/libs/numeric/odeint/doc/steppers.qbk
==============================================================================
--- sandbox/odeint/libs/numeric/odeint/doc/steppers.qbk (original)
+++ sandbox/odeint/libs/numeric/odeint/doc/steppers.qbk 2010-04-20 17:48:28 EDT (Tue, 20 Apr 2010)
@@ -31,15 +31,6 @@
that the stepper gets informed about any change of the state size by calling its
`adjust_size` method.
-[*Template Parameters]
-
-[table
- [[Parameter] [] [default value] [description]]
- [[class Container] [required] [-] [Type of container that stores the state of the system]]
- [[class Time] [optional] [double] [Type of the time variable in the ode]]
- [[class Traits] [optional] [container_traits< Container >] [container_traits used by the stepper]]
-]
-
[*Associated Types]
[table
[[] [] [Description]]
@@ -111,10 +102,6 @@
(e.g. `vector`), it has to be assured that the stepper gets informed about any
change of the state size by calling its `adjust_size` method.
-[*Template Parameters]
-
-Same as for /basic steppers/ above.
-
[*Associated Types]
Same as for /basic steppers/ above.
@@ -184,10 +171,6 @@
If the error is small enough the timestep is accepted and possibly an increased
stepsize is proposed.
-[*Template Parameters]
-
-Same as for /basic steppers/ above.
-
[*Associated Types]
Same as for /basic steppers/ above.
@@ -281,12 +264,22 @@
[section stepper_euler]
-[*Concept:] Basic stepper
+[*Concept:] [link boost_sandbox_numeric_odeint.stepper.concepts.basic_stepper Basic stepper]
-[*Accuracy:] That means the produced solution is accurate up to order 1.
+[*Accuracy:] The produced solution is accurate up to order 1.
[*Complexity:] This method uses 1 function evaluation.
+[*Template Parameters:]
+[template tpl_parameter_table_[]
+[table
+ [[Parameter] [Default Value] [Description]]
+ [[class Container] [no default value] [Type of container that stores the state of the system]]
+ [[class Time] [double] [Type of the time variable in the ode]]
+ [[class Traits] [container_traits< Container >] [container_traits used by the stepper]]
+]]
+[tpl_parameter_table_]
+
The Euler algorithm used in this class performs one integration
step according to the formula:
[: x(t+dt) = x(t) + dt*f(x,t)]
@@ -298,12 +291,16 @@
[section stepper_rk4]
-[*Concept:] Basic stepper
+[*Concept:] [link boost_sandbox_numeric_odeint.stepper.concepts.basic_stepper Basic stepper]
[*Accuracy:] The produced solution is accurate up to order 4.
[*Complexity:] This method uses 4 function evaluations.
+[*Template Parameters:]
+
+[tpl_parameter_table_]
+
The Runge-Kutta 4 algorithm is /the/ classical method to integrate odes.
The [@http://en.wikipedia.org/wiki/Runge%e2%80%93Kutta_methods#Explicit_Runge.E2.80.93Kutta_methods
Butcher Tableau] for this method is as follows:
@@ -325,13 +322,17 @@
[section stepper_rk5_ck]
-[*Concept:] Error stepper
+[*Concept:] [link boost_sandbox_numeric_odeint.stepper.concepts.error_stepper Error stepper]
[*Accuracy:] The produced solution is accurate up to order 5 and the estimated
error is also of order 5.
[*Complexity:] This method uses 6 function evaluation.
+[*Template Parameters:]
+
+[tpl_parameter_table_]
+
The Runge-Kutta method of order 5 with Cash-Karp coefficients is a good trade-off
between numerical effort and obtained accuracy with error estimation.
It is the all-round method and suitable for most problems.
@@ -342,13 +343,17 @@
[section stepper_rk78_fehlberg]
-[*Concept:] Error Stepper
+[*Concept:] [link boost_sandbox_numeric_odeint.stepper.concepts.error_stepper Error Stepper]
[*Accuracy:] The produced solution is accurate up to order 7 and the estimated
error is of order 8.
[*Complexity:] This method uses 13 function evaluations.
+[*Template Parameters:]
+
+[tpl_parameter_table_]
+
The Runge-Kutta 78 Fehlberg method is a high-order algorithm that produces very
good accuracy but for the cost of high numerical effort.
Whenever extra-ordinarily high precision is required, you can fall back to this
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