E-CodeNewton's method for nonlinear systems — a TI-84 Plus CE program
NEWTSYS is a TI-BASIC program for the TI-84 Plus CE. Type F1(X,Y)=0 and F2(X,Y)=0 and a starting point. Each iteration is shown: X, Y, F1, F2 and the correction DX, DY from J*D=-F, with the Jacobian worked out numerically on the first step.
Says so when the Jacobian is singular or it doesn't converge.
What it asks for and what it shows
It asks for 4 values at its prompts. In the example below it shows X, Y, F1, F2, F1X, F1Y, F2X, F2Y, JACOBIAN (NUM), ITERATION 1, J*D, CONVERGED.
Example run
One of its oracle test cases. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Input 1 | X²+Y²-4 |
| Input 2 | XY-1 |
| Input 3 | 2 |
| Input 4 | 0.5 |
| The screen shows | |
X= | 1.931851653 |
Y= | 0.5176380902 |
F1= | 0 |
F2= | 0 |
F1X= | 4 |
F1Y= | 1 |
F2X= | 0.5 |
F2Y= | 2 |
| Text | JACOBIAN (NUM) |
| Text | ITERATION 1 |
J*D= | -F,NEW=OLD+D |
| Text | CONVERGED |
How it's checked
5 test cases, each checked against an independent method. Replayed key by key on a virtual TI-84 Plus CE, they make 52 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-84 Plus CE calculator and pick “Newton's method for two nonlinear equations, step by step” (NEWTSYS).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
Related programs
- Simplex method for linear programming, step by step
- Newton-Raphson root finder
- Bisection root finder
- Numerical integration lab
- Newton's method with an iteration table
All TI-84 Plus CE math programs · All TI-84 Plus CE programs