Improved Version of EULER2
Posted 1/8/2005

Purpose: EULER2 is a freeware program we developed in class on Friday, 1/7/2005, for the TI-83 or TI-83 Plus calculator. The revised version below is somewhat more efficient and clearly shows both the x value and the estimated y value for each step of Euler’s Method.

Note: It is assumed that you have already stored the differential equation (as a function of x and y) in your calculator’s Y₁ function.

Remember that the y results are estimates. In general, they will be more accurate if you use a smaller step size (h value). Of course, if your slope information (Y₁) is a constant, then the solution will be a straight line. In that case, the Euler results will be exactly correct, regardless of the step size.

Program listing:

:ClrHome
:Disp "MR. HANSEN'S"
:Disp "IMPROVED VERSION"
:Disp "OF EULER2 1/8/05"
:Disp ""
:Disp "ENTER INITIAL"
:Disp "CONDITION AND"
:Disp "STEP SIZE:"
:Prompt X,Y,H
:Lbl AA
:Y1®S
:Y+SH®Y
:X+H®X
:Disp "NEW X="
:Disp X
:Disp "NEW ESTIMATED Y:"
:Disp Y
:Pause
:ClrHome
:Goto AA