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RK4\ Runge-Kutta 4th Order ODE Solver {#rk4-runge-kutta-4th-order-ode-solver align=”center”} ================================

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RK4 is a C++ library which implements a simple Runge-Kutta solver for an initial value problem.

The rk4() function does not include any error estimator. It takes a single step at a time, requiring the user to control the step size.

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”}

RK4 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.

RKF45, a C++ library which implements the Runge-Kutta-Fehlberg ODE solver.

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.

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

• rk4.cpp, the source code.
• rk4.hpp, the include file.

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

• rk4_prb.cpp, a sample calling program.
• rk4_prb_output.txt, the output file.
• rk4_prb.png, an image of the solution.

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

• RK4 takes one Runge-Kutta step for a scalar ODE.
• RK4VEC takes one Runge-Kutta step for a vector ODE.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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

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Last revised on 09 October 2013.