Euler/Heun reconciliation

Hello

I am trying to understand a program to bring the first itarations of a function like below with the euler and heun method:

On hpcalc, there seems to be something very close: http://www.hpcalc.org/details.php?id=6344

It would be perfect, if I want to enter the equation, start and time end as well as the initial value of y, and the number of iterations.

for example, for this formula

T0 = 1, tmax is 1.5, n = 2, y0 = 0-> euler should give 0.25 and 0.5125, heun 0.2563 and 0.5313

Maybe I'm wrong but I havn't found a way to enter the above formula in this program.

Can someone with a better knowledge of programming the 50g please check if this is not possible and how programs could be adapted if necessary?

The files for both methods are attached.

PS. Euler's method in Maple looks like:

Hi Teleboy.

You can do (in mode about):

"F x → y xend n.
«
'F(x,y)' f = SET
xEnd x - n / 'h' STO
1. FOR n a
' h * F (x, y) + y' 'y' STO
'x' STO h +.
NEXT
There
»
»
"Euler" STO

Use:

' x-1/x * y' 1. 0 1.5 2. Euler

Returns

0.5125

If you need intermediate results:

"F x → y xend n.
«
'F(x,y)' f = SET
xEnd x - n / 'h' STO
1. FOR n a
' h * F (x, y) + y' 'y' STO
'x' STO h +.
x y 2. →LIST
NEXT
→LIST n
»
»
"Euler" STO

' x-1/x * y' 1. 0-1.5 10. Euler

Returns

{{1,05.05} {1.1.100119047619} {1.15.150568181818} {1.2.20152173913} {1,25.253125} {1,3.3055} {1,35.35875} {1,4.412962962963} {1,45.468214285714} {1,5.524568965517}}

Note that you could solve this symbolicaly with DESOLVE (exact mode)

' d1Y (X) + Y (X) / X = X' 'Y' DESOLVE

With the x 0 y0 conditions you get:

'(X^3-1) /(3*X) | X = 3/2 '-> 19/36 ~ 0.527777...

Tags: HP Tablets

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