Commit 037950ca authored by Henry's avatar Henry
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Updated docs

parent ee7284d4
......@@ -34,10 +34,7 @@ Description
Cash, J.R.,
Karp, A.H.
ACM Transactions on Mathematical Software, vol. 16, 1990, pp. 201–222.
\endverbatim
Based on code from:
\verbatim
"Solving Ordinary Differential Equations I: Nonstiff Problems,
second edition",
Hairer, E.,
......
......@@ -34,10 +34,7 @@ Description
Prince, P. J.,
Journal of Computational and Applied Mathematics,
6 (1), 1980: pp. 19-26.
\endverbatim
Based on code from:
\verbatim
"Solving Ordinary Differential Equations I: Nonstiff Problems,
second edition",
Hairer, E.,
......
......@@ -34,8 +34,6 @@ Description
Fehlberg, E.,
NASA Technical Report 315, 1969.
Based on code from:
\verbatim
"Solving Ordinary Differential Equations I: Nonstiff Problems,
second edition",
Hairer, E.,
......@@ -48,31 +46,6 @@ Description
and allows to perform an adapdive step-size control using these two order
without the need of re-evaluation.
\f{align}{
k_1 &= h f(t_k, y_k) \\
k_2 &= h f(t_k + \frac{1}{4}h, y_k + \frac{1}{4}k_1) \\
k_3 &= h f(t_k + \frac{3}{8}h, y_k + \frac{3}{32}k_1 + \frac{9}{32}k_2) \\
k_4 &= h f(t_k + \frac{12}{13}h, y_k + \frac{1932}{2197}k_1
\frac{7200}{2197}k_2 + \frac{7296}{2197}k_3) - \\
k_5 &= h f(t_k + h, y_k + \frac{439}{216}k_1 - 8k_2 + \frac{3680}{513}k_3 -
\frac{845}{4104}k_4) \\
k_6 &= h f(t_k + \frac{1}{2}h, y_k - \frac{8}{27}k_1 + 2k_2 -
\frac{3544}{2565}k_3 + \frac{1859}{4104}k_4 - \frac{11}{40}k_5) \\
\f}
Which yields the following update-steps for the 4th and 5th order:
\f{align}{
\Delta_4 &= \frac{25}{216}k_1 + \frac{1408}{2565}k_3 +
\frac{2197}{4101}k_4 - \frac{1}{5}k_5 \\
\Delta_5 &= \frac{16}{135}k_1 + \frac{6656}{12825}k_3 +
\frac{9}{50}k_5 + \frac{2}{55}k_6
\f}
The difference between the 5th and 4th order (\f$\epsilon = \left|\Delta_5
- \Delta_4\right|\f$) can be used to determine if the stepsize \f$h\f$ needs
to be adjusted.
SourceFiles
RKF45.C
......
......@@ -27,7 +27,6 @@ Class
Description
L-stable embedded Rosenbrock ODE solver of order (3)4.
Based on code from:
\verbatim
"Solving Ordinary Differential Equations II: Stiff
and Differential-Algebraic Problems, second edition",
......@@ -37,7 +36,7 @@ Description
Springer-Verlag, Berlin. 1996.
\endverbatim
Also provided are the constants from:
The default constants are from:
\verbatim
"Implementation of Rosenbrock Methods"
Shampine, L. F.,
......@@ -46,6 +45,8 @@ Description
with which the scheme is more accurate than with the L-Stable coefficients
for small step-size but less stable for large step-size.
The L-Stable scheme constants are provided commented-out in Rosenbrock43.C
SourceFiles
Rosenbrock43.C
......
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