Numerical integration: Difference between revisions
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exit /*stick a fork in it, we're done.*/ |
exit /*stick a fork in it, we're done.*/ |
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/*──────────────────────────────────LEFT_RECT subroutine────────────────*/ |
/*──────────────────────────────────LEFT_RECT subroutine────────────────*/ |
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left_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
left_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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sum=0 |
sum=0 |
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do x=a by h for n |
do x=a by h for n |
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sum=sum+f(x) |
sum=sum+f(x) |
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end |
end /*x*/ |
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return sum*h |
return sum*h |
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/*──────────────────────────────────MIDPOINT_RECT subroutine────────────*/ |
/*──────────────────────────────────MIDPOINT_RECT subroutine────────────*/ |
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midpoint_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
midpoint_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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sum=0 |
sum=0 |
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do x=a+h/2 by h for n |
do x=a+h/2 by h for n |
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sum=sum+f(x) |
sum=sum+f(x) |
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end |
end /*x*/ |
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return sum*h |
return sum*h |
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/*──────────────────────────────────RIGHT_RECT subroutine───────────────*/ |
/*──────────────────────────────────RIGHT_RECT subroutine───────────────*/ |
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right_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
right_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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sum=0 |
sum=0 |
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do x=a+h by h for n |
do x=a+h by h for n |
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sum=sum+f(x) |
sum=sum+f(x) |
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end |
end /*x*/ |
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return sum*h |
return sum*h |
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/*──────────────────────────────────SIMPSON subroutine──────────────────*/ |
/*──────────────────────────────────SIMPSON subroutine──────────────────*/ |
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simpson: procedure expose test; parse arg a,b,n; |
simpson: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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sum1=f(a+h/2) |
sum1=f(a+h/2) |
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| ⚫ | |||
sum2=0 |
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| ⚫ | |||
sum1=sum1+f(a+h*x+h*.5) |
sum1=sum1+f(a+h*x+h*.5) |
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sum2=sum2+f(a+x*h) |
sum2=sum2+f(a+x*h) |
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end |
end /*x*/ |
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return h*(f(a)+f(b)+4*sum1+2*sum2)/6 |
return h*(f(a)+f(b)+4*sum1+2*sum2)/6 |
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/*──────────────────────────────────TRAPEZOID subroutine────────────────*/ |
/*──────────────────────────────────TRAPEZOID subroutine────────────────*/ |
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trapezoid: procedure expose test; parse arg a,b,n; |
trapezoid: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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sum=0 |
sum=0 |
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do x=a to b by h |
do x=a to b by h |
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sum=sum+h*(f(x)+f(x+h))*.5 |
sum=sum+h*(f(x)+f(x+h))*.5 |
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end |
end /*x*/ |
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return sum |
return sum |
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/*──────────────────────────────────F subroutine────────────────────────*/ |
/*──────────────────────────────────F subroutine────────────────────────*/ |
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f: procedure expose test; parse arg z |
f: procedure expose test; parse arg z |
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if test==1 then return z**3 |
if test==1 then return z**3 |
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if test==2 then return 1/z |
if test==2 then return 1/z |
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return z</lang> |
return z</lang> |
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'''output''' |
'''output''' |
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<pre> |
<pre> |
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