RKF45 is a FORTRAN90 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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
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.
CWG_ODE, a FORTRAN77 library which contains three ODE solvers, by C William Gear.
NMS, a FORTRAN90 library which includes a wide variety of numerical software.
ODE, a FORTRAN90 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.
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You can go up one level to the FORTRAN90 source codes.