Solution of Singular and Nonsingular Initial and Boundary Value Problems by Modified Variational Iteration Method

Table 5

(Error estimates). The absolute error between the exact and the series solutions. Higher accuracy can be obtained by introducing some more components of the series solution.

𝑡𝑗	𝐸−14
	0.01	0.02	0.04	0.1	0.2	0.5
−1	2.80886 𝐸−12	1.79667 𝐸−10	1.15235 𝐸−8	2.83355 𝐸−6	1.83899 𝐸−4	4.74681 𝐸−14
−0.8	6.27276 𝐸−12	4.01362 𝐸−10	2.57471 𝐸−8	6.33178 𝐸−6	4.10454 𝐸−3	1.04489 𝐸−14
−0.6	6.08402 𝐸−12	3.90188 𝐸−10	2.25663 𝐸−8	6.18024 𝐸−6	4.02299 𝐸−3	1.03093 𝐸−14
−0.4	1.16573 𝐸−13	7.41129 𝐸−11	4.82756 𝐸−8	1.23843 𝐸−6	8.53800 𝐸−4	2.46302 𝐸−14
−0.2	5.53446 𝐸−12	3.53395 𝐸−10	2.25663 𝐸−8	5.47485 𝐸−6	3.47264 𝐸−4	8.35783 𝐸−14
0	8.63198 𝐸−12	5.53357 𝐸−10	2.54174 𝐸−8	8.65197 𝐸−6	5.54893 𝐸−3	1.37353 𝐸−14
0.2	5.56222 𝐸−12	3.55044 𝐸−10	2.27779 𝐸−8	5.60362 𝐸−6	3.63600 𝐸−4	9.29612 𝐸−14
0.4	1.14353 𝐸−13	7.14928 𝐸−11	4.49107 𝐸−8	1.03370 𝐸−7	5.93842 𝐸−5	9.61260 𝐸−14
0.6	6.06182 𝐸−12	3.87551 𝐸−10	2.47218 𝐸−8	5.97562 𝐸−6	3.76275 𝐸−4	8.79002 𝐸−14
0.8	6.23945 𝐸−12	3.99519 𝐸−10	2.55127 𝐸−8	6.18881 𝐸−6	3.92220 𝐸−4	9.36404 𝐸−14
1	2.79776 𝐸−12	1.78946 𝐸−10	1.14307 𝐸−8	2.77684 𝐸−6	1.76607 𝐸−4	4.28986 𝑥𝑖