jburkardt

RKF45\ Runge-Kutta-Fehlberg ODE Solver {#rkf45-runge-kutta-fehlberg-ode-solver align=”center”} ===============================

---

RKF45 is a C++ library which implements the Watt and Shampine RKF45 ODE solver.

The RKF45 ODE solver is a Runge-Kutta-Fehlberg algorithm for solving an ordinary differential equation, with automatic error estimation using rules of order 4 and 5.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

RKF45 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a PYTHON version.

Related Data and Programs: {#related-data-and-programs align=”center”}

GSL, a C++ library which includes routines for solving differential equations.

NMS, a FORTRAN90 library which includes the DDRIV package of ODE solvers.

ODE, a C++ library which solves a system of ordinary differential equations, by Shampine and Gordon.

ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.

RK4, a C++ library which applies the fourth order Runge-Kutta algorithm to estimate the solution of an ordinary differential equation at the next time step.

TEST_ODE, a FORTRAN90 library which contains routines which define some test problems for ODE solvers.

Reference: {#reference align=”center”}

1. Erwin Fehlberg,\ Low-order Classical Runge-Kutta Formulas with Stepsize Control,\ NASA Technical Report R-315, 1969.
2. Lawrence Shampine, Herman Watts, S Davenport,\ Solving Non-stiff Ordinary Differential Equations - The State of the Art,\ SIAM Review,\ Volume 18, pages 376-411, 1976.
3. The source code for Shampine and Watt’s original FORTRAN77 routine is available at http://www.netlib.org/ode/ the NETLIB ODE web site.

Source Code: {#source-code align=”center”}

• rkf45.cpp, the source code;
• rkf45.hpp, the include file;

Examples and Tests: {#examples-and-tests align=”center”}

RKF45_PRB includes a number of examples of how to use RKF45.

• rkf45_prb.cpp, a sample calling program;
• rkf45_prb_output.txt, the output file;

RKF45_PRB2 includes an example in which the ODE includes parameters ALPHA, BETA, and GAMMA, which the user wants to set at run time. The example shows one way in which these values can be shared with the derivative routine.

• rkf45_prb2.cpp, a sample calling program;
• rkf45_prb2_output.txt, the output file;

List of Routines: {#list-of-routines align=”center”}

• R4_ABS returns the absolute value of an R4.
• R4_EPSILON returns the round off unit for floating arithmetic.
• R4_FEHL takes one Fehlberg fourth-fifth order step.
• R4_MAX returns the maximum of two real values.
• R4_MIN returns the minimum of two real values.
• R4_RKF45 carries out the Runge-Kutta-Fehlberg method.
• R4_SIGN returns the sign of a real number.
• R8_ABS returns the absolute value of a double precision number.
• R8_EPSILON returns the R8 round off unit.
• R8_FEHL takes one Fehlberg fourth-fifth order step.
• R8_MAX returns the maximum of two R8s.
• R8_MIN returns the minimum of two R8s.
• R8_RKF45 carries out the Runge-Kutta-Fehlberg method.
• R8_SIGN returns the sign of a real number.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

---

Last revised on 20 November 2007.