Solving Separable Nonlinear Equations Using LU Factorization

Table 1

Newton iterations for Example 1.

𝑘	𝑦1^(𝑘)−𝑦^∗1	𝑦2^(𝑘)−𝑦^∗2	‖𝑦^(𝑘)−𝑦^(𝑘−1)‖
0	1.0000𝑒−001	−1.0000𝑒−001	—
1	−2.3657𝑒−003	4.4412𝑒−003	1.4624𝑒−001
2	−5.7794𝑒−006	1.8337𝑒−008	5.0292𝑒−003
3	2.5508𝑒−012	7.5073𝑒−012	5.7794𝑒−006