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https://github.com/jacobwilliams/dop853
Modern Fortran Edition of Hairer's DOP853 ODE Solver. An explicit Runge-Kutta method of order 8(5,3) for problems y'=f(x,y); with dense output of order 7
https://github.com/jacobwilliams/dop853
dop853 fortran fortran-package-manager ode runge-kutta
Last synced: about 1 month ago
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Modern Fortran Edition of Hairer's DOP853 ODE Solver. An explicit Runge-Kutta method of order 8(5,3) for problems y'=f(x,y); with dense output of order 7
- Host: GitHub
- URL: https://github.com/jacobwilliams/dop853
- Owner: jacobwilliams
- License: other
- Created: 2015-12-30T22:59:01.000Z (about 9 years ago)
- Default Branch: master
- Last Pushed: 2023-01-29T19:33:47.000Z (about 2 years ago)
- Last Synced: 2024-11-08T03:09:33.243Z (3 months ago)
- Topics: dop853, fortran, fortran-package-manager, ode, runge-kutta
- Language: Fortran
- Homepage:
- Size: 1.4 MB
- Stars: 50
- Watchers: 6
- Forks: 13
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
============
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](https://github.com/jacobwilliams/dop853).
## Status
[](https://github.com/jacobwilliams/dop853/releases/latest)
[](https://github.com/jacobwilliams/dop853/actions)
[](https://codecov.io/gh/jacobwilliams/dop853)
[](https://github.com/jacobwilliams/dop853/commits/master)
## Example
Basic use of the solver is shown here. The main methods in the `dop853_class` are `initialize()` and `integrate()`.
```fortran
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_example
```
The result is:
```
x =100.00 y = -0.1360372426E+01 0.1325538438E+01
```
For dense output, see the example in the `src/tests` directory.
## Building DOP853
A [Fortran Package Manager](https://github.com/fortran-lang/fpm) 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:
```toml
[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](https://github.com/Fortran-FOSS-Programmers/ford), run:
```
ford dop853.md
```
## 3rd Party Dependencies
The unit tests require [pyplot-fortran](https://github.com/jacobwilliams/pyplot-fortran) which will be automatically downloaded by FPM.
## Documentation
The latest API documentation for the `master` branch can be found [here](https://jacobwilliams.github.io/dop853/). This is generated by processing the source files with [FORD](https://github.com/Fortran-FOSS-Programmers/ford).
## References
1. E. Hairer, S.P. Norsett and G. Wanner, "[Solving ordinary
Differential Equations I. Nonstiff Problems](http://www.unige.ch/~hairer/books.html)", 2nd edition.
Springer Series in Computational Mathematics,
Springer-Verlag (1993).
2. Ernst Hairer's website: [Fortran and Matlab Codes](http://www.unige.ch/~hairer/software.html)
## License
* [Original license for Hairer's codes](http://www.unige.ch/~hairer/prog/licence.txt).
* The updates are released under a [similar BSD-style license](https://raw.githubusercontent.com/jacobwilliams/dop853/master/LICENSE).
## See also
* [numbalsoda](https://github.com/Nicholaswogan/numbalsoda) Python wrapper to this code.