Numerical integration: Difference between revisions
Content added Content deleted
m (→{{header|REXX}}: changed spelling of trapezoid to trapezium, fixed trapezium (function) returned value.) |
m (→{{header|REXX}}: changed the trapezium function's returned value, changed some comments.) |
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| Line 3,603: | Line 3,603: | ||
$=0 |
$=0 |
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do x=a by h for n; $=$+f(x); end /*x*/ |
do x=a by h for n; $=$+f(x); end /*x*/ |
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return $*h/1 /*return |
return $*h/1 /*return the number with no trailing 0s*/ |
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/*────────────────────────────────────────────────────────────────────────────*/ |
/*────────────────────────────────────────────────────────────────────────────*/ |
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midpoint_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
midpoint_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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$=0 |
$=0 |
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do x=a+h/2 by h for n; $=$+f(x); end /*x*/ |
do x=a+h/2 by h for n; $=$+f(x); end /*x*/ |
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return $*h/1 /*return |
return $*h/1 /*return the number with no trailing 0s*/ |
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/*────────────────────────────────────────────────────────────────────────────*/ |
/*────────────────────────────────────────────────────────────────────────────*/ |
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right_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
right_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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$=0 |
$=0 |
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do x=a+h by h for n; $=$+f(x); end /*x*/ |
do x=a+h by h for n; $=$+f(x); end /*x*/ |
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return $*h/1 /*return |
return $*h/1 /*return the number with no trailing 0s*/ |
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/*────────────────────────────────────────────────────────────────────────────*/ |
/*────────────────────────────────────────────────────────────────────────────*/ |
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Simpson: procedure expose test; parse arg a,b,n; h=(b-a)/n |
Simpson: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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| Line 3,619: | Line 3,619: | ||
@=0; do x=1 for n-1; $=$+f(a+h*x+h*.5); @=@+f(a+x*h); end /*x*/ |
@=0; do x=1 for n-1; $=$+f(a+h*x+h*.5); @=@+f(a+x*h); end /*x*/ |
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return h |
return h*(f(a) + f(b) + 4*$ + 2*@)/6 /*return the number with no trailing 0s*/ |
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/*────────────────────────────────────────────────────────────────────────────*/ |
/*────────────────────────────────────────────────────────────────────────────*/ |
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trapezium: procedure expose test; parse arg a,b,n; h=(b-a)/n |
trapezium: procedure expose test; parse arg a,b,n; h=(b-a)/n |
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$=0 |
$=0 |
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do x=a |
do x=a by h for n; $=$+(f(x)+f(x+h))*.5; end /*x*/ |
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return $* |
return $*h/1 /*return the number with no trailing 0s*/</lang> |
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'''output''' |
'''output''' |
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<pre> |
<pre> |
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| Line 3,632: | Line 3,632: | ||
right_rectangular(0, 1, 100) = 0.255025 |
right_rectangular(0, 1, 100) = 0.255025 |
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Simpson(0, 1, 100) = 0.25 |
Simpson(0, 1, 100) = 0.25 |
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trapezium(0, 1, 100) = 0. |
trapezium(0, 1, 100) = 0.250025 |
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─────────────────────────────test 2────────────────────────────── |
─────────────────────────────test 2────────────────────────────── |
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| Line 3,639: | Line 3,639: | ||
right_rectangular(1, 100, 1000) = 4.5569810575146761472 |
right_rectangular(1, 100, 1000) = 4.5569810575146761472 |
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Simpson(1, 100, 1000) = 4.6051703849571421725 |
Simpson(1, 100, 1000) = 4.6051703849571421725 |
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trapezium(1, 100, 1000) = |
trapezium(1, 100, 1000) = 4.6059860575146761454 |
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─────────────────────────────test 3────────────────────────────── |
─────────────────────────────test 3────────────────────────────── |
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| Line 3,646: | Line 3,646: | ||
right_rectangular(0, 5000, 5000000) = 12500002.5 |
right_rectangular(0, 5000, 5000000) = 12500002.5 |
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Simpson(0, 5000, 5000000) = 12500000 |
Simpson(0, 5000, 5000000) = 12500000 |
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trapezium(0, 5000, 5000000) = |
trapezium(0, 5000, 5000000) = 12500000 |
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─────────────────────────────test 4────────────────────────────── |
─────────────────────────────test 4────────────────────────────── |
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| Line 3,653: | Line 3,653: | ||
right_rectangular(0, 6000, 5000000) = 18000003.6 |
right_rectangular(0, 6000, 5000000) = 18000003.6 |
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Simpson(0, 6000, 5000000) = 18000000 |
Simpson(0, 6000, 5000000) = 18000000 |
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trapezium(0, 6000, 5000000) = |
trapezium(0, 6000, 5000000) = 18000000 |
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</pre> |
</pre> |
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