Casio fx-CG50 field manual for IB Math
Euler's method for coupled systems
Use sequence tables to apply Euler's method to two linked first-order differential equations.
Use Euler's method with step size h=0.2 for the coupled system x′=y, y′=−x−0.4y, x(0)=1, y(0)=0. Approximate x(1) and y(1).
From the MAIN MENU open Recursion. Press (TYPE), then (an+1) so both sequences are defined recursively.
Let an store x and bn store y. Sequence references come from the (n.an···) menu: inserts an and inserts bn. On the first line enter an + 0.2bn ( , then + 0.2, then ) and press . On the second line build bn + 0.2(-an - 0.4bn) the same way.
Press (SET), then (a0) so the initial terms are numbered from zero. Use Start = 0 and End = 5 (five steps of size 0.2 reach t=1), and set the initial terms a0 = 1, b0 = 0.
EXIT back, press (TABLE), and read both values in the row n=5.
x(1)≈0.638 and y(1)≈−0.779.
Your turn
Work each one on your calculator, then check the answer.
- 1
Use Euler's method with h=0.2 for x′=0.5y, y′=−0.5x, x(0)=2, y(0)=0, to approximate x(1) and y(1).
- 2
Use Euler's method with h=0.1 for x′=−y, y′=x−0.5y, x(0)=1, y(0)=1, to approximate x(0.5) and y(0.5).
- 3
A predator–prey system has x′=0.4x−0.1xy, y′=0.05xy−0.2y with x(0)=10, y(0)=5. Use Euler's method with h=0.1 to approximate x(0.5) and y(0.5).