EULER (Graphical Version) - HP 48

Introduction
This program plots an approximate solution for the differential equation ${\hbox{dy}\over \hbox{dx}}=\hbox{f(x,y\ )}$ using Euler's method. These solutions can be superimposed on a slopefield by running the Slope Field program first. Previous graphs are not cleared for comparison purposes.

If you have not used one of the programs posted on this website before, you should read through the information in the Intro to Programming section first.

The Program
Note: The main program, EULG, will call a subprogram, SUB3. Both programs are given below.

<<RCLF 'flags' STO

-19 SF -2 SF

"INITIAL X" ":X:" INPUT

OBJ 'X' STO

"INITIAL Y" ":Y:" INPUT

OBJ 'Y' STO

"STEP SIZE" ":H:" INPUT

OBJ 'H' STO

"# ITERATIONS" :N:"

INPUT OBJ 'N' STO

{# 0d # 0d} PVIEW DRAX

SUB3 {U V X Y K H N}

PURGE flags STOF 'flags'

PURGE >>

ENTER 'EULG' STO {This stores the program under variable name EULG.}

<<1 N FOR C FUNC

NUM 'K' STO

X H + 'U' STO

H K * Y + 'V' STO

U VV2 X YV2

LINE U 'X' STO

V 'Y' STO NEXT>>

ENTER 'SUB3' STO {This stores the program under the variable name SUB3}

Running the Program

You will need to enter a function f(x,y) into a variable called FUNC before running the program. Follow the instructions in

<<RCLF 'flags' STO
-19 SF -2 SF
"INITIAL X" ":X:" INPUT
OBJ 'X' STO
"INITIAL Y" ":Y:" INPUT
OBJ 'Y' STO
"STEP SIZE" ":H:" INPUT
OBJ 'H' STO
"# ITERATIONS" :N:"
INPUT OBJ 'N' STO
{# 0d # 0d} PVIEW DRAX
SUB3 {U V X Y K H N}
PURGE flags STOF 'flags'
PURGE >>

ENTER 'EULG' STO	{This stores the program under variable name EULG.}


<<1 N FOR C FUNC
NUM 'K' STO
X H + 'U' STO
H K * Y + 'V' STO
U VV2 X YV2
LINE U 'X' STO
V 'Y' STO NEXT>>

ENTER 'SUB3' STO	{This stores the program under the variable name SUB3}