Casio fx-CG50 field manual for IB Math
Euler's method
Use a sequence table to iterate Euler's method for a first-order differential equation.
Use Euler's method for y′=√tanxy, y(1)=1, with step size h=0.1, to approximate y(1.3).
From the MAIN MENU open Recursion. Press (SET UP) and check Angle is Rad: the recurrence contains anx, so a Deg setting gives the wrong table. Press , then (TYPE), then (an+1) so both sequences are defined recursively.
Let an store the x-values and bn store the y-values. Sequence references come from the (n.an···) menu: inserts n, inserts an, inserts bn. On the first line press , type + 0.1, and press . On the second line build bn + 0.1bn ÷ √(tan(an)) the same way, with for bn and for an.
Press (SET), then (a0) so the initial terms are numbered from zero. Use Start = 0 and End = 3 (three steps of size 0.1 take x from 1 to 1.3), and set the initial terms a0 = 1, b0 = 1. Keep End at the step count: a larger End makes the table step x past 2π≈1.571, where tanx<0 and √tanx is non-real, and the table errors.
EXIT back, press (TABLE), and read the bn value in the row n=3.
y(1.3)≈1.23 (the table shows 1.229343).
Your turn
Work each one on your calculator, then check the answer.
- 1
Use Euler's method with h=0.1 for y′=√tanxy, y(1)=2, to approximate y(1.2).
- 2
Use Euler's method with h=0.1 for y′=y√cosx, y(1)=1, to approximate y(1.4).
- 3
Use Euler's method with h=0.1 for y′=√1−x2y, y(0.6)=1, to approximate y(0.9).