Euler's Method of Numerical Integration

This program for HP 39gs (HP 40gs) applies Euler's method to the solution of the differential equation Y'=f(X,Y) on the X-interval [A,B]. The program prompts for input of A, B, an initial value Y = Y(A) and the number N of steps. It displays the resulting approximate value for Y(B). The function f is stored in the Function Aplet "F1(X)". To key in the program, Press [SHIFT] [PROGRAM] and give it a name - Type in EU, for example, and press [ENTER] key.

Type in the following program sequence:

(B-A)/N
Press {STO>}
H:
Press [ENTER] key
Y
Press {STO>}
Z:1
Press {STO>}
I:E
Press {STO>}
X:
Press [ENTER] key
FOR I=1 TO N STEP 1;
Press [ENTER] key
Z+F1(X)*H
Press {STO>}
Z:
Press [ENTER] key
X+H
Press {STO>}
X:
Press [ENTER] key
END:
Press [ENTER] key
MSGBOX Z:
Press [ENTER] key

The screen should look like this:

Press [SHIFT] [PROGRAM] to return to the program list.
You can download this Euler Aplet for HP39g+, HP39gs or HP40gs.  Go to [SHIFT] [PROGRAM] and {RECV} to upload into your calculator.

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How the Euler program work?
Following are variables used...
A = x0 (First value).
B = Final Estimate for Y.
Y = y0 (Initial value of Y).
N = Steps.
H = Size of each step.
X = Increment (of H) after each step.
F1(X) = Differential Equation stored in Symbolic Function.
Z = Result
User provide A, B, Y and N.
User provide the Differential Equation.
Calculate H.
Loop through the steps to calculate Z.
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To check that you have enter the program correctly. 

Enter Y into F1(x), so the differential equation in questionis Y'= Y, with solution Y = e^(X)+1. Run the program with A=0, B=0.5,Y=1, N=5. 

Press [SYMB]
Enter the following into F1(X):

Press the [Home]
Enter the following variables:

And Press [ENTER].
Where A=0, B=0.5,Y=1, N=5.

Type RUN EU and press [ENTER].

The result will be prompted.

The result should be 2.1168.