01292020, 09:07 PM
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 HP45, 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 HP45). If this happens, simply switch order of the equations and try again.
source: tech briefs, C.Rubin, May 1 1975, pg. 89
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SOLUTION: Use a minicalculator and the program given here. The program was developed for the HP45, 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 HP45). 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
STO3
x⇄y
STO 4
RCL×6
RCL 3
RCL×5
+
STO2
RCL 4
RCL×7
RCL 3
RCL×8
+
RCL 2
RCL×9
+
STO1
RCL 1
RCL 2
RCL 3
RCL 4
source: tech briefs, C.Rubin, May 1 1975, pg. 89
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