TI-Nspire CX II 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).
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)+0.2·u2(n-1) with initial term 1, and use to reach the domain line and change its start to 0, so it reads 0≤n≤99. Starting at n=0 makes n count completed steps, so t=0.2n and the target t=1 is row n=5.
Add the y-sequence the same way: u2(n)=u2(n-1)+0.2(-u1(n-1)-0.4·u2(n-1)) with initial term 0 and the same 0 domain start. Both updates read the previous step's u1 and u2, so the coupled values advance together.
Press to split the screen with a table of both sequences, and scroll to row n=5: the u1 column holds x(1) and the u2 column holds y(1). The graph pane plots both sequences as points, showing the damped oscillation as it develops.
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).