(45) Calc program simplifies simulataneous equations

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  PROBLEM: Solve four simultaneous differential equations in less than four minutes

  SOLUTION: Use a minicalculator and the program given here. The program was developed for the HP-45, but can be adapted to other calculators with similar storage capacity. An equivalent program could be written for a calculator with less storage capacity, but execution time would be longer.
  The program is based on the Gauss algorithm for linear equations and solves a set of simultaneous equations of the form:
┏                   ┓
┃ a₁₁ a₁₂ a₁₃ a₁₄ ┃ ┃x₁┃  ┃c₁┃
┃ a₂₁ a₂₂ a₂₃ a₂₄ ┃ ┃x₂┃  ┃c₂┃
┃ a₃₁ a₃₂ a₃₃ a₃₄ ┃ ┃x₃┃=┃c₃┃
┃ a₄₁ a₄₂ a₄₃ a₄₄ ┃ ┃x₄┃  ┃c₄┃
┗                   ┛
where the aij and ci terms are known. The xi terms are the unknowns.
The four answers are displayed in the last four steps of the program: RCL 1 displays x1, RCL 2 displays x2, RCL 3 displays x3, RCL 4 displays x4. The only possible problem for an independent set of equations is that division by zero may occur (this is indicated by a blinking display on the HP-45). If this happens, simply switch order of the equations and try again.

Code:


a₁₂
STO 9
a₁₃
STO 8
a₁₄
STO 7
c₁
STO 1
a₁₁
STO÷9
STO÷8
STO÷7
STO÷1
a₂₁
STO 3
RCL×8
RCL 7
RCL×3
RCL 1
RCL×3
c₂
-
STO 2
R↓
a₂₄
-
STO 6
R↓
a₂₃
-
RCL 3
RCL×9
a₂₂
-
STO÷6
STO÷2
÷
STO 5
a₃₁
STO 3
RCL×9
a₃₂
-
STO 4
RCL×6
RCL 3
RCL×7
-
a₃₄
+
RCL 4
RCL×2
RCL 3
RCL×1
-
c₃
+
RCL 4
RCL×5
RCL 3
RCL×8
-
a₃₃
+
ENTER↑
R↓
÷
STO 3
R↓
x⇄y
÷
STO 4
a₄₁
ENTER↑
RCL×9
a₁₂
-
ENTER↑
RCL×5
a₄₃
+
R↓
R↓
RCL×8
x⇄y
R↓
-
RCL×4
LAST X
RCL×3
R↓
R↓
R↓
RCL×1
+
x⇄y
R↓
x⇄y
RCL×2
-
c₄
-
R↓
RCL×6
-
a₄₁
RCL×7
+
a₄₄
-
x⇄y
R↓
÷
ENTER↑
RCL×4
STO-3
x⇄y
STO 4
RCL×6
RCL 3
RCL×5
+
STO-2
RCL 4
RCL×7
RCL 3
RCL×8
+
RCL 2
RCL×9
+
STO-1
RCL 1
RCL 2
RCL 3
RCL 4

source: tech briefs, C.Rubin, May 1 1975, pg. 89

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