(12C) Numeric Solver
04-13-2017, 01:50 AM
Post: #1
 Dwight Sturrock Member Posts: 125 Joined: Dec 2013
(12C) Numeric Solver
This solver uses Newton's method to solve f(x)=0. It is an adaptation of the HP-25 solver (HP-25 Application Programs, Chapter 5). The program uses registers 0, 1, 2, 3 and 4.

Enter the program as listed- it will occupy lines 1 through 38. The formula to be solved will start on line 39 and must end with the command GTO 17.

EXAMPLE-

Solve ln x + 3x -10.8074 = 0

Starting with line 38 displayed, enter the formula:

LN
LST X
3
*
+
1
0
.
8
0
7
4
-
GTO 17

Store an initial guess in register 1:

1
STO 1

Store the desired tolerance in register 2:

EEX
5
CHS
STO 2

Press R/S to solve. Result: 3.21336

PHP Code:
CLX    STO 0    RCL 1    GTO 39    //xeq formulaROLL DN    STO 4    1    STO 0    RCL 1    RCL 1    EEX    5    /    STO 3    +    GTO 39    //xeq formulaX=0    GTO 37    RCL 0    X=0    GTO 05    ROLL DN    RCL 4    /    1    -    1/X    RCL 3    x     STO – 1    2    Y^X    SQRT    RCL 2    X<=Y       //x is less than or equal to y    GTO 01    RCL 1    //answerR/S                //formula...GT0 17
04-14-2017, 04:33 PM (This post was last modified: 04-14-2017 04:33 PM by Dieter.)
Post: #2
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: (12C) Numeric Solver
(04-13-2017 01:50 AM)Dwight Sturrock Wrote:  This solver uses Newton's method to solve f(x)=0. It is an adaptation of the HP-25 solver (HP-25 Application Programs, Chapter 5).

The program calculates h (in R3) as x/1E5. This does not work for x=0 since it yields h=0 and so the derivative gets zero, leading to a division by zero.

But this can be fixed easily:

...
RCL 1
RCL 1
X=0?
e^x

EEX
4
/
STO 3
...

After this change the GTOs of course need to be updated.

One more tip: instead of 2 [Y^X] always use [ENTER] [x]. This is much faster and exact.

Dieter
04-14-2017, 10:15 PM
Post: #3
 Dwight Sturrock Member Posts: 125 Joined: Dec 2013
RE: (12C) Numeric Solver
(04-14-2017 04:33 PM)Dieter Wrote:
(04-13-2017 01:50 AM)Dwight Sturrock Wrote:  This solver uses Newton's method to solve f(x)=0. It is an adaptation of the HP-25 solver (HP-25 Application Programs, Chapter 5).

The program calculates h (in R3) as x/1E5. This does not work for x=0 since it yields h=0 and so the derivative gets zero, leading to a division by zero.

But this can be fixed easily:

...
RCL 1
RCL 1
X=0?
e^x

EEX
4
/
STO 3
...

After this change the GTOs of course need to be updated.

One more tip: instead of 2 [Y^X] always use [ENTER] [x]. This is much faster and exact.

Dieter

Thanks Dieter, I'll try your enhancements and repost.
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