Approximate Solutions for Nonlinear Initial Value Problems Using the Modified Variational Iteration Method

Table 1

The approximate solution (5.6) in comparison with the exact solution (5.2) if 𝑡=0.5.

𝑥	𝑢exact	𝑢VHP	|𝑢exact−𝑢VHP|
−50	2.59461×10^−11	2.58455×10^−11	1.00576×10^−13
−40	3.85074×10^−9	3.83581×10^−9	1.4929×10^−11
−30	5.715×10^−7	5.69285×10^−7	2.21575×10^−9
−20	0.000084811	0.000084482	3.28572×10^−7
−10	0.0124317	0.0123887	4.29767×10^−5
0	0.651355	0.651164	1.91128×10^−4
10	0.996406	0.996441	3.44391×10^−5
20	0.999976	0.999976	2.55845×10^−7
30	1	1	1.7249×10^−9
40	1	1	1.16228×10^−11
50	1	1	7.81597×10^−14