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https://github.com/zoziha/rkf45
Fehlberg fourth-fifth order Runge-Kutta method. (rkf45)
https://github.com/zoziha/rkf45
fehlberg fortran fortran-package-manager fourth-fifth-order ode rkf45 runge-kutta
Last synced: 24 days ago
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Fehlberg fourth-fifth order Runge-Kutta method. (rkf45)
- Host: GitHub
- URL: https://github.com/zoziha/rkf45
- Owner: zoziha
- License: mit
- Created: 2021-11-01T12:49:28.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2023-08-02T14:02:11.000Z (over 1 year ago)
- Last Synced: 2024-01-29T14:16:50.201Z (12 months ago)
- Topics: fehlberg, fortran, fortran-package-manager, fourth-fifth-order, ode, rkf45, runge-kutta
- Language: Fortran
- Homepage: http://www.netlib.org/ode/rkf45.f
- Size: 29.3 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# RKF45
[](LICENSE)
`rkf45` is based on Fehlberg fourth-fifth order Runge-Kutta method.
## Usage
Only FPM is supported, other build systems can copy source files (`./src/rkf45.F90`) directly,
and `ifort` and `gfortran` compilers are tested.
To use `rkf45` within your `fpm` project, add the following lines to your `fpm.toml` file:
```toml
[dependencies]
rkf45 = { git="https://github.com/zoziha/rkf45" }
```
### Example
```sh
> fpm run --example --all # run the examples
```
```fortran
!> Solve a Bernoulli differential equation using rkf45:
!> y' = y - 2*x/y
program example_rkf45
use rkf45_module, only: rkf45, rk
integer, parameter :: neqn = 1
real(rk) :: t = 0.0_rk, t_out = 0.0_rk, y(neqn)
real(rk) :: relerr = epsilon(1.0), abserr = epsilon(1.0)
integer :: flag = 1
integer :: iwork(5), i, n_step = 5
real(rk) :: work(3 + 6*neqn)
real(rk) :: t_start = 0.0_rk, t_end = 1.0_rk
print "(A/)", "rkf45: solve a Bernoulli differential equation, y' = y - 2*x/y"
print "(A6, *(A18))", "T", "Y", "Y_Exact", "Error"
y = 1.0
do i = 1, n_step
t = t_start + (i - 1)*(t_end - t_start)/n_step
t_out = t_start + i*(t_end - t_start)/n_step
call rkf45(fcn, neqn, y, t, t_out, relerr, abserr, flag, work, iwork)
print "(F6.2, 3ES18.10)", t, y(1), fx(t), fx(t) - y(1)
end do
contains
!> Evaluates the derivative for the ODE
subroutine fcn(t, y, yp)
real(rk), intent(in) :: t
real(rk), intent(in) :: y(:)
real(rk), intent(out) :: yp(:)
yp(1) = y(1) - 2.0_rk*t/y(1)
end subroutine fcn
!> Exact solution
real(rk) function fx(t)
real(rk), intent(in) :: t
fx = sqrt(1.0_rk + 2.0_rk*t)
end function fx
end program example_rkf45
!> rkf45: solve a Bernoulli differential equation, y' = y - 2*x/y
!>
!> T Y Y_Exact Error
!> 0.20 1.1832159758E+00 1.1832159758E+00 0.0000000000E+00
!> 0.40 1.3416407108E+00 1.3416407108E+00 0.0000000000E+00
!> 0.60 1.4832396507E+00 1.4832397699E+00 1.1920928955E-07
!> 0.80 1.6124514341E+00 1.6124515533E+00 1.1920928955E-07
!> 1.00 1.7320506573E+00 1.7320507765E+00 1.1920928955E-07
```
## Links
- [netlib/rkf45](http://www.netlib.org/ode/rkf45.f)
- [John Burkardt/rkf45(Fixed Format)](https://people.math.sc.edu/Burkardt/f77_src/rkf45/rkf45.html)
- [John Burkardt/rkf45(Free Format)](https://people.math.sc.edu/Burkardt/f_src/rkf45/rkf45.html)
- [jacobwilliams/rksuite](https://github.com/jacobwilliams/rksuite)
- [jacobwilliams/runge-kutta-fortran](https://github.com/jacobwilliams/runge-kutta-fortran)