Gauss-Chebyshev Quadrature

[Namir]

This is a program that calculates the area under a function using the Gauss-Chebyshev quadrature. The program prompts you for:

1. The lower limit of the integral, A.
2. The upper limit of the integral, B.
3. The number of points to use for the calculations, N. This is also the order of Chebyshev polynomial used in the calculations.

LBL E has the code for the function you want to integrate. Currently, the program integrates the function f(x)=1/x. The version of the quadrature implemented has equal weights of pi/N.

The memory map is:

Code:


R0 = A
R1 = B
R2 = N
R4 = T1 = (B-A)/2
R5 = T2 = (B+A)/2
R6 = T3 = pi/N/2
R7 = Sum = sum of f(T1*X+T2)
R8 = Y = COS((2i-1)*T3)
R9 = X = f(T1*X+T2)

Code:

1    LBL "GCQD"        
2    LBL A        
3    "A?"        
4    PROMPT        
5    STO 00        
6    "B?"        
7    PROMPT        
8    STO 01        
9    "N?"        
10    PROMPT        
11    STO 02        
12    RCL 01        
13    RCL 00        
14    -        
15    2        
16    /        
17    STO 04        # calculate T1
18    RCL 01        
19    RCL 00        
20    +        
21    2        
22    /        
23    STO 05        # calculate T2
24    PI        
25    RCL 02        
26    /        
27    2        
28    /        
29    STO 06        # calculate T3
30    RAD        
31    0        
32    STO 07        # Sum = 0
33    LBL 00        # start loop -----------------------
34    RCL 02        
35    2        
36    *        
37    1        
38    -        
39    RCL 06        
40    *        
41    COS        
42    STO 08        # calculate Y
43    RCL 04        
44    *        
45    RCL 05        
46    +        
47    STO 09        # calculate X
48    XEQ E        # calculate f(x)
49    1        
50    STO- 02        # N = N - 1
51    RCL 08        
52    X^2        
53    -        
54    SQRT        
55    *        
56    STO+ 07        # sum = sum + F * sqrt(1-Y*Y)
57    RCL 02        
58    X#0?        
59    GTO 00        # resume loop iterations
60    RCL 07        
61    RCL 04        
62    *        
63    RCL 06        
64    *        
65    2        
66    *        
67    BEEP        
68    RTN        
69    LBL E        # subroutine for f(x)
70    1/X        
71    RTN