RK4
Runge-Kutta 4th Order ODE Solver

RK4 is a FORTRAN77 library which implements a simple Runge-Kutta solver for an initial value problem.

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

Licensing:

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

Languages:

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:

CWG_ODE, a FORTRAN77 library which implements three ODE solvers by C William Gear.

DRIV, a FORTRAN77 library which solves real or complex systems of ordinary differential equations;

NMS, a FORTRAN77 library which includes the DDRIV package of ODE solvers.

ODE, a FORTRAN77 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 FORTRAN77 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:

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:

• rk4.f, the source code.
• rk4.sh, BASH commands to compile the source code.

Examples and Tests:

• rk4_prb.f, a sample calling program.
• rk4_prb.sh, BASH commands to compile and run the sample program.
• rk4_prb_output.txt, the output file.
• rk4_prb.png, an image of the solution.

List of Routines:

• RK4 takes one Runge-Kutta step.
• RK4VEC takes one Runge-Kutta step for a vector system.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.