This is a modern Fortran (2003/2008) implementation of Hairer's DOP853 ODE solver. The original FORTRAN 77 code has been extensively refactored, and is now object-oriented and thread-safe, with an easy-to-use class interface. DOP853 is an explicit Runge-Kutta method of order 8(5,3) due to Dormand & Prince (with stepsize control and dense output).
This project is hosted on GitHub.
Basic use of the solver is shown here. The main methods in the dop853_class are initialize() and integrate().
program dop853_example
use dop853_module, wp => dop853_wp
use iso_fortran_env, only: output_unit
implicit none
integer,parameter :: n = 2 !! dimension of the system
real(wp),parameter :: tol = 1.0e-12_wp !! integration tolerance
real(wp),parameter :: x0 = 0.0_wp !! initial x value
real(wp),parameter :: xf = 100.0_wp !! endpoint of integration
real(wp),dimension(n),parameter :: y0 = [0.0_wp,0.1_wp] !! initial y value
type(dop853_class) :: prop
real(wp),dimension(n) :: y
real(wp),dimension(1) :: rtol,atol
real(wp) :: x
integer :: idid
logical :: status_ok
x = x0 ! initial conditions
y = y0 !
rtol = tol ! set tolerances
atol = tol !
!initialize the integrator:
call prop%initialize(fcn=fvpol,n=n,status_ok=status_ok)
if (.not. status_ok) error stop 'initialization error'
!now, perform the integration:
call prop%integrate(x,y,xf,rtol,atol,iout=0,idid=idid)
!print solution:
write (output_unit,'(1X,A,F6.2,A,2E18.10)') &
'x =',x ,' y =',y(1),y(2)
contains
subroutine fvpol(me,x,y,f)
!! Right-hand side of van der Pol's equation
implicit none
class(dop853_class),intent(inout) :: me
real(wp),intent(in) :: x
real(wp),dimension(:),intent(in) :: y
real(wp),dimension(:),intent(out) :: f
real(wp),parameter :: mu = 0.2_wp
f(1) = y(2)
f(2) = mu*(1.0_wp-y(1)**2)*y(2) - y(1)
end subroutine fvpol
end program dop853_exampleThe result is:
x =100.00 y = -0.1360372426E+01 0.1325538438E+01
For dense output, see the example in the src/tests directory.
A Fortran Package Manager manifest file is included, so that the library and tests cases can be compiled with FPM. For example:
fpm build --profile release
fpm test --profile release
To use dop853 within your FPM project, add the following to your fpm.toml file:
[dependencies]
dop853 = { git="https://github.com/jacobwilliams/dop853.git" }By default, the library is built with double precision (real64) real values. Explicitly specifying the real kind can be done using the following processor flags:
| Preprocessor flag | Kind | Number of bytes |
|---|---|---|
REAL32 |
real(kind=real32) |
4 |
REAL64 |
real(kind=real64) |
8 |
REAL128 |
real(kind=real128) |
16 |
For example, to build a single precision version of the library, use:
fpm build --profile release --flag "-DREAL32"
To generate the documentation using FORD, run:
ford dop853.md
The unit tests require pyplot-fortran which will be automatically downloaded by FPM.
The latest API documentation for the master branch can be found here. This is generated by processing the source files with FORD.
- E. Hairer, S.P. Norsett and G. Wanner, "Solving ordinary Differential Equations I. Nonstiff Problems", 2nd edition. Springer Series in Computational Mathematics, Springer-Verlag (1993).
- Ernst Hairer's website: Fortran and Matlab Codes
- Original license for Hairer's codes.
- The updates are released under a similar BSD-style license.
- numbalsoda Python wrapper to this code.