TI-84 Plus CE 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).
Press and switch from FUNCTION to SEQ. Also switch from SEQUENTIAL to SIMUL so the coupled recurrences update from the same previous row.
Press and use SEQ(n+1). Let u ( ) store time, v ( ) store x, and w ( ) store y. Enter nMin=0, u(n+1)=u(n)+0.2, u(0)=0, v(n+1)=v(n)+0.2w(n), v(0)=1, w(n+1)=w(n)+0.2(-v(n)-0.4w(n)), and w(0)=0. Type n with . In w(n+1) the leading sign inside the parentheses is a negative, not a subtraction: press (the (-) key) for it, and only for the -0.4w(n) term. The full key sequence is .
Open table setup with . Set both Indpnt and Depend to Ask. Then open the table with , type 5 in the n column, and press . Move across to v(n) and w(n), pressing on each cell to calculate both values.
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).