rk4

rk4, a FORTRAN90 code which implements a fourth-order Runge-Kutta method to solve an ordinary differential equation (ODE).

Licensing:

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

Languages:

rk4 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version and an R version.

Related Data and Programs:

midpoint_explicit, a FORTRAN90 code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method.

midpoint_fixed, a FORTRAN90 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a fixed point method for the implicit equation.

nms, a FORTRAN90 code which includes the DDRIV package of ODE solvers.

ode, a FORTRAN90 code which solves a system of ordinary differential equations, by Shampine and Gordon.

rk4_test

rkf45, a FORTRAN90 code which implements the Runge-Kutta-Fehlberg ODE solver.

test_ode, a FORTRAN90 code 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.f90, the source code.
• rk4.sh, compiles the source code.