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

Table 3

Comparison of numerical solutions.

𝑥𝑟	𝑦(𝑥) (Laplace method)	𝑦𝑁(𝑥) (present method)
0	0.3	0.3
0.1	0.0835845348	0.08358453484
0.2	−0.105091915	−0.1050919158
0.3	−0.266020303	−0.2660203036
0.4	−0.399977948	−0.3999779482
0.5	−0.508314810	−0.5083148108
0.6	−0.592890689	−0.5928906891
0.7	−0.656065502	−0.6560655028
0.8	−0.700676939	−0.7006769399
0.9	−0.729970850	−0.7299708508
1	−0.747476077	−0.7474760775