- #1
CMJ96
- 50
- 0
Homework Statement
I'd like to solve the following integral using the 2D trapezoidal method in fortran 95
$$I=\int^{1.40406704}_{-1.40406704} \int^{x+1.40406704}_{x-1.40406704} exp(x+y) dy dx$$
Homework Equations
$$I= \frac{h}{2} \left(f_0+ 2 \sum_{i=1}^{n-1} f_i +f_n \right)+O(h^2) $$
The Attempt at a Solution
So I have wrote my program below, attempting to use a nested do loop to calculate the integral over the two dimensions. However I am not sure how to use the result of my do loop to arrive at a final answer, I'm also not sure if my loop is entirely correct, here is a copy of my script
program trap2d
implicit none
real :: hy, hx, c, d, integralx, integraly, func, I_numeric,x,y,integral
integer :: nx,ny,ix,iy
c=-(1.140406704)
d=(1.140406704)
ny=1000
nx=1000
hx=(d-c)/nx
integralx=0.0
do ix=1,nx-1
x=c+ix*hx
hy=((x+1.140406704)-(x-1.140406704))/ny
integraly=0.0
do iy=1,ny-1
y=x-1.140406704+iy*hy
integraly=integraly+hy*func(x,y)
end do
integralx=integralx+hx*integraly
end do
end program
function func(x,y)
implicit none
real :: func,x,y
func=exp(x+y)
end function func