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

Table 1

Comparison of the absolute errors of Example 1.

𝑥𝑟	Exact	Error analysis (|𝑦−𝑦𝑁|)
		𝑁=5	𝑁=8	𝑁=10
0	0	0	0	0
0.1	0.9983341665	4.62𝐸−8	3.08𝐸−11	4.33𝐸−14
0.2	0.1986693308	6.12𝐸−7	8.72𝐸−11	1.03𝐸−13
0.3	0.2955202067	4.28𝐸−7	1.45𝐸−11	1.66𝐸−13
0.4	0.3894183423	2.29𝐸−7	1.82𝐸−10	2.21𝐸−13
0.5	0.4794255386	4.23𝐸−7	1.65𝐸−10	2.71𝐸−13
0.6	0.5646424734	4.03𝐸−7	2.62𝐸−10	3.15𝐸−13
0.7	0.6442176872	3.32𝐸−7	3.01𝐸−12	2.29𝐸−13
0.8	0.7173560909	5.66𝐸−7	3.07𝐸−10	3.85𝐸−13
0.9	0.7833260096	8.87𝐸−6	5.68𝐸−9	9.73𝐸−13
1	0.841470984	1.43𝐸−5	1.22𝐸−8	1.57𝐸−11