Texas Instruments TI-83 Manual page 24

Program DFIELD
Output: A direction field for
system
dx dy
= g(x, y), = h(x, y). In the later case, we take
dt dt
f (x, y) = h(x, y)/g(x, y).
Input: f (X, Y ) as the Y
:ClrDraw
:FnOff
:(Xmax Xmin)/10 → S
:Xmin+S → X
:Ymin+S → Y
:Lbl 1
:X S/5 → A
:Y SY /5 → B
1
:X + S/5 → C
:Y + SY /5 → D
1
:Line(A,B,C,D)
:Y + S → Y
:If Y <Ymax
:Goto 1
:X + S → X
:Ymin→ Y
:If X ≥ Xmax
:Stop
:Goto 1
Program EULER
Output: An approximate solution using Euler's method
dy
to = f (x, y), y = y(x
0
dx
Input: f (X, Y ) as the Y
y = y(x ), H and B as h and b in Euler's method
0 0
:FnOff
:Disp "X0"
:Input X
:Disp "Y0"
:Input Y
:Disp "H"
:Input H
:Disp "B"
:Input B
:Lbl 1
:Disp "X="
:Disp X
:Disp "Y="
:Disp Y
:Pause
:Y + HY → Y
1
:X + H → X
dy
= f (x, y) or for the
dx
variable.
1
) on the interval [x , b].
0 0
variable, X0 as x , Y0 as
1 0
:If X ≤ B + H
Goto 1
Stop
Program EULERG
Output: The graph of an approximate solution to y =
f (x, y), y(0) = x on the interval [x
0
method.
Input: f (X, Y ) as the Y
y = y(x ), H as h in Euler's method. Set the RANGE
0 0
variables so that x
min
:ClrDraw
:FnOff
:Disp "X0"
:Input X
:Disp "Y0"
:Input Y
:Disp "B"
:Input B
:Disp "H"
:Input H
:Lbl 1
:X → P
:Y → Q
:Pt-On(X,Y)
:P → X
:Q → Y
:Y + HY → Y
1
:X + H → X
:If X < B + H
:Goto 1
:Stop
Program EULERS
Output: A graph of an approximate solution to the sys-
tem of differential equations
P (x, y, t), X(t ) = X
0
method.
Input: P (X, Y, T ) as the Y
Y variable, H as h in Euler's method. Set the range
2
variables as desired.
:FnOff
:ClrDraw
:(Xmax Xmin)/H → N
:Disp "X0"
:Input X
:Disp "Y0"
:Input Y
:Disp "H"
53
, B] using Euler's
0
variable, X0 as x
1 0
= x and x = B.
0 max
dX
= P (x, y, t),
dt
, Y (t ) = Y using Euler's
0 0 0
variable, Q(X, Y, T ) as the
1
, Y0 as
dY
=
dt