(HP 42S) (DM42) Double integral using Gaussian method

05272020, 01:46 PM
(This post was last modified: 06012020 09:32 AM by rawi.)
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(HP 42S) (DM42) Double integral using Gaussian method
HP 42S / DM42 has an integration function that is not recursive. If you want to integrate a function that includes an integral you get an error message. So it is not able to compute double integrals.
The program INT2 computes double integrals using Gaussian method. The program uses a solution for single integrals given by Thomas Klemm in the Museum of HP calculators for the HP 11C (https://www.hpmuseum.org/forum/thread38...t=Integral). How to use it: 1. Put the function you want to integrate under label "FU". The function must take Y from Y register and X from X register and deliver f(X,Y) in Xregister. The example given is the function e^(X²Y²/2). 2. Put the number of subintervals in register 00. The more subintervals you use the more precise the result will be. 3. Put the limits of the integral in the stack: Lower limit of variable Y in T, upper limit in Z, lower limit of variable X in Y, upper limit in X 4. Execute INT2 The program does not use the integral function. So in principle it should be possible to use it in the "FUN"function and thus have triple integrals. But this was not tried yet. Registers used: 00, 1021 Example: The example with the limits of 0 and 1 for Y and 1 and 2 for X and four subintervals delivers with the DM 42 in about 1 second 0.11572940947. HP Prime delivers 0.11572940908. So these results have 9 digits in common. 00 { 186Byte Prgm } 01▸LBL "INT2" 02 STO 11 03  04 RCL 00 05 ÷ 06 STO 10 07 2 08 ÷ 09 STO+ 11 10 0.6 11 SQRT 12 × 13 STO 13 14 R↓ 15 STO 21 16  17 RCL 00 18 ÷ 19 STO 15 20 CLX 21 STO 12 22 RCL 00 23 1ᴇ3 24 ÷ 25 1 26 + 27 STO 14 28▸LBL 00 29 RCL 11 30 RCL 13 31 + 32 XEQ 01 33 5 34 × 35 STO 12 36 RCL 11 37 RCL 13 38  39 XEQ 01 40 5 41 × 42 STO 12 43 RCL 11 44 XEQ 01 45 8 46 × 47 STO 12 48 RCL 10 49 STO+ 11 50 ISG 14 51 GTO 00 52 RCL 12 53 × 54 18 55 ÷ 56 RTN 57▸LBL 01 58 STO 20 59 RCL 21 60 STO 16 61 RCL 15 62 2 63 ÷ 64 STO+ 16 65 0.6 66 SQRT 67 × 68 STO 18 69 CLX 70 STO 17 71 RCL 00 72 1ᴇ3 73 ÷ 74 1 75 + 76 STO 19 77▸LBL 02 78 RCL 16 79 RCL 18 80 + 81 RCL 20 82 XEQ "FU" 83 5 84 × 85 STO 17 86 RCL 16 87 RCL 18 88  89 RCL 20 90 XEQ "FU" 91 5 92 × 93 STO 17 94 RCL 16 95 RCL 20 96 XEQ "FU" 97 8 98 × 99 STO 17 100 RCL 15 101 STO+ 16 102 ISG 19 103 GTO 02 104 RCL 17 105 × 106 18 107 ÷ 108 RTN 109 END 00 { 17Byte Prgm } 01▸LBL "FU" 02 X↑2 03 +/ 04 X<>Y 05 X↑2 06 +/ 07 2 08 ÷ 09 + 10 E↑X 11 RTN 12 END 

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