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Ingy döt Net 2013-04-10 23:57:08 -07:00
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Task/Numerical-integration/Logo/numerical-integration.logo Normal file
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to i.left :fn :x :step
output invoke :fn :x
end
to i.right :fn :x :step
output invoke :fn :x + :step
end
to i.mid :fn :x :step
output invoke :fn :x + :step/2
end
to i.trapezium :fn :x :step
output ((i.left :fn :x :step) + (i.right :fn :x :step)) / 2
end
to i.simpsons :fn :x :step
output ( (i.left :fn :x :step)
+ (i.mid :fn :x :step) * 4
+ (i.right :fn :x :step) ) / 6
end
to integrate :method :fn :steps :a :b
localmake "step (:b - :a) / :steps
localmake "sigma 0
; for [x :a :b-:step :step] [make "sigma :sigma + apply :method (list :fn :x :step)]
repeat :steps [
make "sigma :sigma + (invoke :method :fn :a :step)
make "a :a + :step ]
output :sigma * :step
end
to fn2 :x
output 2 / (1 + 4 * :x * :x)
end
print integrate "i.left "fn2 4 -1 2 ; 2.456897
print integrate "i.right "fn2 4 -1 2 ; 2.245132
print integrate "i.mid "fn2 4 -1 2 ; 2.496091
print integrate "i.trapezium "fn2 4 -1 2 ; 2.351014
print integrate "i.simpsons "fn2 4 -1 2 ; 2.447732