Fortran 90 Euler Scheme for Radioactive Decay

[ksx2098]

Homework Statement

in fortran 90 write a program to using the euler scheme to solve the differential equation for decay of a radioactive substance

dx/dt = -j*x

solving the equation we get

x = e^(-j*t)

following info is given

2. Homework Equations and values

t0 = 0.0
tF = 10.0
tStep = 0.1
x(0) = 1+0i
j = 3.0

The Attempt at a Solution

PROGRAM EULER
!
INTEGER :: I,N
REAL :: t, x
REAL, PARAMETER :: t0 = 0.0, tF = 10.0, tStep = 0.1, j = 3.0
!
!Calc N
!
N = INT((tF-t0)/tStep + SPACING((tF-t0)/tStep)) + 1 ! trip count
!
!set initial values
!
t = t0
x = 0.0
!
!Calculate x with time
!
DO I + 1, N+1
      PRINT *, t, x
      x = x + tStep * f(x,t)
      t = t + tStep
ENDDO
!
END PROGRAM EULER
!
FUNCTION f(x,t)
!
REAL :: t, x
REAL, PARAMETER :: j = 3.0
!
f = EXP( -1.0 * j * t)
!
END FUNCTION f(x,t)

no errors upon compiling

my x value ends up being 2*t

i think the problem is in the DO loop

 

[dlgoff]

Shouldn't DO I + 1, N+1
be Do I=1,N+1

 

[Mene]

.


Your attempt at solving this problem using the Euler scheme for radioactive decay is a good start. However, there are a few things that can be improved upon.

Firstly, in the DO loop, the counter variable I should start from 0 instead of 1. This is because the initial value of x is given at t=0, so we need to account for that in our loop.

Secondly, the function f(x,t) should take into account the decay constant j, which is given as 3.0 in the problem statement. So the correct function should be f(x,t) = -j*x.

Thirdly, the initial value of x is given as 1+0i, which implies that x is a complex number. However, in your code, x is declared as a real number. You can declare it as a complex number using the COMPLEX data type in Fortran.

Lastly, the Euler scheme is an approximation method and it is not very accurate for solving differential equations. It would be better to use a more accurate method like the Runge-Kutta method.

Overall, your attempt is a good start, but it can be improved upon by taking into account these suggestions.