Solving a stiff initial-value problem – HP 48g Graphing Calculator User Manual
Page 229
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6
. Enter the initial value for the solution variable.
7. Enter an acceptable error tolerance.
8
. (Optional:) Enter a step size. Normally, the solver computes an
appropriate step size.
9. Press SOLVE.
Example:
Solve this equation for y{\) given that ?/(0) = 2:
y' = i + y
CTfsoivEi m
© T (T) © Y (ENTER)
© T(ENTER)0 (ENTER) 1
(ENTER)(g)
2
(ENTER)
SOLVE V(TJ=FCT,V)
F=
■ T+Y '
INDEP: T INIT:
0
FINAL: 1
SDLN:
V INIT:
2
FINHLif
TDL:.0001 STEP:
Df
It _ STIFF
6.15477759086
BBgmHHmiiiiiiiiiiHiiiim^
How accurate is the answer? The general solution to the differential
equation
y' = t + y
19
t
y = ce
t -
1
Where c is an arbitrary constant. The given initial conditions were
2
= ce° — 0 — 1. Solving for c and substituting back into the general
solution, the solution equation is
y = 3e* — t — I
Solving for !/(l), returns 3e — 1 — 1 = 6.15484548538. Comparing the
results you can see there is an error of approximately 0.000068 which
is well within the specified error tolerance of
0
.
0001
.
Solving a Stiff Initial-Value Problem
Some differential equations may seem to take forever to solve. If this
happens, the equations may be stiff. Use the stiff function to solve the
equation.
To use the stiff fynction:
1. Press (7^(S0LVE~)
2. Select So I ye dit f eq„
Differential Equations 19-3