Help with solving first order ODE using a simple Fortran code, please

[joseph2015]

I am trying to solve the following first order ODE using a simple Fortran code :

$$ ds/dt=k_i * \sqrt{v}$$

where both (ki) and (v) are variables depending on (h) as follows

$$ k_i=\sqrt{χ/h^2}$$
$$v= \mu h$$

where (μ) and (χ) are constants. (the arbitrary values of each of them can be seen from the code attached).

Note: h changes from 100 to 1 with -1 reduction

Now after writing the code, I would like to plot (s) as a function of (h). but what I will get is not a single plot, but a series of plots depending on the number of timesteps. the issue has to do with loops, but I am not sure how to get a single plot of (s) against (h) as it grows over a period of time.

program height
    implicit none

    double precision ki, t, v, s, a, x, tend, dt
    integer count,h,nstep
    real mu
    REAL, PARAMETER :: Pi = 3.1415927
    tend   = 100
    dt     = 10
    nstep  = tend/dt

    write(*,*) 'end time for the integration: ', tend
    write(*,*) 'integration time step: ', dt
    write(*,*) 'number of time steps: ', nstep

    open(30, file='height.agr')
 
    x      = 1.99
    s      = 1.0e-2
    mu     = 2.34
    t      = 0.0

    write(30,*) s, real(h*1.8e+4)

    ! START to Integrate.

    write(*,*) 'Start time integration (', nstep, ' steps) ...'

    do count = 1, nstep
        ! update the time
        t = t + dt

!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       do h  =100,1,-1
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 
          v  =mu*h
          ki =sqrt((x)/h**2)
          a  = ki*sqrt(v)
          s  = s+dt*a

            write(30,*) s, real(h)
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       end do
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    end do

    write(*,*) 'end'
    close(30)
    100  format(d14.8,1x,d14.8)
end program height

 

[BvU]

Your write statement is in an inner loop, so you get 100 writes for every time step.
What's worse, s is incremented 100 times for every time step too.
And the outer loop is done only 10 times.

What is it you want to do ?

 

[joseph2015]

Your write statement is in an inner loop, so you get 100 writes for every time step.
What's worse, s is incremented 100 times for every time step too.
And the outer loop is done only 10 times.

What is it you want to do ?

Thank you very much for your answer

I am trying to follow the change of s as a function of time and h, then plot s vs h.
for example: if s is a strength of a material, while h is height (from 100 to 1cm), I would like to plot s vs h for 100 years time.

Kind regards,

Joseph

 

[BvU]

My guess is you want to swap the loops and reset t to 0 in the outer loop. That way you get s(t) with h as a parameter.
And I'd do 100 steps in t and 10 steps in h.

And with double $ to delimit the $\TeX$ source you get displayed math:
$$ \frac {ds}{dt}=k_i \sqrt v$$ $$ k_i=\sqrt{\chi/h^2}=\frac {\sqrt \chi }{h } $$

 

[joseph2015]

My guess is you want to swap the loops and reset t to 0 in the outer loop. That way you get s(t) with h as a parameter.
And I'd do 100 steps in t and 10 steps in h.

And with double $ to delimit the $\TeX$ source you get displayed math:
$$ \frac {ds}{dt}=k_i \sqrt v$$ $$ k_i=\sqrt{\chi/h^2}=\frac {\sqrt \chi }{h } $$

I will try that, thank you very much