(35S) Gauss-Legendre 16-Point Integration

[Gerald H]

Useful if you need to solve a function containing an integral.

1 LBL E
2 CLx
3 STO D
4 RCL B
5 RCL A
6 STO G
7 -
8 RCL C
9 STO E
10 RCL+ E
11 /
12 STO F
13 STO+ G
14 16
15 STO I
16 RCL G
17 RCL (I)
18 RCL* F
19 STO H
20 -
21 XEQ T001
22 STO K
23 RCL G
24 RCL+ H
25 XEQ T001
26 RCL+ K
27 DSE I
28 RCL* (I)
29 STO+ D
30 DSE I
31 GTO E016
32 RCL F
33 STO+ G
34 DSE E
35 GTO E013
36 STO* D
37 RCL D
38 RTN
39 1►I
40 271524594118E-13►(I)
41 2►I
42 989400934992E-12►(I)
43 3►I
44 622535239386E-13►(I)
45 4►I
46 944575023073E-12►(I)
47 5►I
48 951585116825E-13►(I)
49 6►I
50 865631202388E-12►(I)
51 7►I
52 124628971256E-12►(I)
53 8►I
54 755404408355E-12►(I)
55 9►I
56 149595988817E-12►(I)
57 10►I
58 617876244403E-12►(I)
59 11►I
60 169156519395E-12►(I)
61 12►I
62 458016777657E-12►(I)
63 13►I
64 182603415045E-12►(I)
65 14►I
66 281603550779E-12►(I)
67 15►I
68 189450610455E-12►(I)
69 16►I
70 950125098376E-13►(I)
71 RTN

To initialize XEQ E039, filling memory slots 1 to 16 with the MAGIC NUMBERS.

Store lower limit of integration in A, upper limit in B & number of divisions of the area to be found in C, eg 1 for speed, higher integers for more accuracy.

Enter the function, taking one real value from the stack & returning a real value, to be integrated as a programme under label T.

Then XEQ E to find the approx integral.