Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

Table 2

Numerical results of Example 2.

𝑥𝑟	Error analysis (𝐸𝑁(𝑥𝑟))
	𝑁=5	𝑁=10	𝑁=15	𝑁=20
0	0	0	1.70𝐸−8	0
0.1	4.62𝐸−2	0	0	0
0.2	5.57𝐸−24	0	1.05𝐸−9	2.23𝐸−25
0.3	2.24𝐸−3	0	0	2.22𝐸−25
0.4	0	3.22𝐸−24	2.91𝐸−11	9.80𝐸−25
0.5	6.00𝐸−25	0	0	1.00𝐸−24
0.6	0	2.51𝐸−24	1.62𝐸−11	1.70𝐸−24
0.7	3.63𝐸−2	4.31𝐸−24	0	1.31𝐸−24
0.8	1.13𝐸−1	1.87𝐸−4	1.80𝐸−24	2.10𝐸−24
0.9	1.46𝐸−1	8.28𝐸−3	1.32𝐸−7	8.50𝐸−24
1	5.93𝐸−1	1.32𝐸−2	4.47𝐸−5	3.68𝐸−24