Data commit

Task/Numerical-integration/BBC-BASIC/numerical-integration.basic

@@ -0,0 +1,71 @@
+      *FLOAT64
+      @% = 12 : REM Column width
+
+      PRINT "Function     Range          L-Rect      R-Rect      M-Rect      Trapeze     Simpson"
+      FOR func% = 1 TO 4
+        READ x$, l, h, s%
+        PRINT x$, ; l " - " ; h, FNlrect(x$, l, h, s%) FNrrect(x$, l, h, s%) ;
+        PRINT FNmrect(x$, l, h, s%) FNtrapeze(x$, l, h, s%) FNsimpson(x$, l, h, s%)
+      NEXT
+      END
+
+      DATA "x^3", 0,    1,     100
+      DATA "1/x", 1,  100,    1000
+      DATA "x",   0, 5000, 5000000
+      DATA "x",   0, 6000, 6000000
+
+      DEF FNlrect(x$, a, b, n%)
+      LOCAL i%, d, s, x
+      d = (b - a) / n%
+      x = a
+      FOR i% = 1 TO n%
+        s += d * EVAL(x$)
+        x += d
+      NEXT
+      = s
+
+      DEF FNrrect(x$, a, b, n%)
+      LOCAL i%, d, s, x
+      d = (b - a) / n%
+      x = a
+      FOR i% = 1 TO n%
+        x += d
+        s += d * EVAL(x$)
+      NEXT
+      = s
+
+      DEF FNmrect(x$, a, b, n%)
+      LOCAL i%, d, s, x
+      d = (b - a) / n%
+      x = a
+      FOR i% = 1 TO n%
+        x += d/2
+        s += d * EVAL(x$)
+        x += d/2
+      NEXT
+      = s
+
+      DEF FNtrapeze(x$, a, b, n%)
+      LOCAL i%, d, f, s, x
+      d = (b - a) / n%
+      x = b : f = EVAL(x$)
+      x = a : s = d * (f + EVAL(x$)) / 2
+      FOR i% = 1 TO n%-1
+        x += d
+        s += d * EVAL(x$)
+      NEXT
+      = s
+
+      DEF FNsimpson(x$, a, b, n%)
+      LOCAL i%, d, f, s1, s2, x
+      d = (b - a) / n%
+      x = b : f = EVAL(x$)
+      x = a + d/2 : s1 = EVAL(x$)
+      FOR i% = 1 TO n%-1
+        x += d/2
+        s2 += EVAL(x$)
+        x += d/2
+        s1 += EVAL(x$)
+      NEXT
+      x = a
+      = (d / 6) * (f + EVAL(x$) + 4 * s1 + 2 * s2)