TI-Nspire CX II 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).
Open the Scratchpad's Graph view ( → B: Graph Scratchpad) and switch to sequence mode: → 3: Graph Entry/Edit → 7: Sequence → 1: Sequence. Let u1 store x: enter u1(n)=u1(n-1)+0.1 with initial term 1, and use to reach the domain line and change it to 0≤n≤3. Starting at n=0 makes n count completed steps, so x=1+0.1n and the target x=1.3 — three steps of size 0.1 from 1 — is row n=3.
Add the y-sequence the same way: u2(n)=u2(n-1)+0.1·u2(n-1)/√(tan(u1(n-1))) with initial term 1 and the same 0≤n≤3 domain: each new y is the old y plus h times the slope y/√tanx, read from the previous step. Ending the domain at the target matters: past x≈1.571 we have tanx<0, so √tanx is non-real and every later row of the sequence errors.
Press to split the screen with a table of both sequences. Row n=3 shows x=1.3 in the u1 column and the Euler approximation in the u2 column. The graph pane plots both sequences as points, so you can also read the approximation off the plot.
y(1.3)≈1.23 (row n=3 shows 1.22934).
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).