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

Table 6

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−16
	0.01	0.02	0.04	0.1	0.2	0.5
−1	7.77156 𝐸−14	1.36557 𝐸−13	8.57869 𝐸−10	2.09264 𝐸−8	1.33823 𝐸−6	3.25944 𝐸−16
−0.8	1.11022 𝐸−15	1.99840 𝐸−13	1.12688 𝐸−11	2.73880 𝐸−9	1.74288 𝐸−7	4.14094 𝐸−16
−0.6	2.22045 𝐸−14	1.09912 𝐸−13	7.28861 𝐸−10	1.78030 𝐸−8	1.14025 𝐸−6	2.79028 𝐸−16
−0.4	1.11022 𝐸−14	2.32037 𝐸−12	1.50302 𝐸−10	3.67002 𝐸−8	2.34944 𝐸−6	5.74091 𝐸−16
−0.2	6.66134 𝐸−14	3.23075 𝐸−12	2.04747 𝐸−10	4.99918 𝐸−9	3.19983 𝐸−6	7.81509 𝐸−16
0	4.44089 𝐸−14	3.49720 𝐸−12	2.24365 𝐸−10	5.47741 𝐸−8	3.50559 𝐸−6	8.55935 𝐸−16
0.2	5.55112 𝐸−14	3.19744 𝐸−12	2.04714 𝐸−10	4.99820 𝐸−8	3.19858 𝐸−6	7.80749 𝐸−16
0.4	3.33067 𝐸−14	2.32037 𝐸−12	1.50324 𝐸−10	3.66815 𝐸−8	2.34706 𝐸−6	5.72641 𝐸−16
0.6	3.33067 𝐸−14	1.12133 𝐸−12	7.28528 𝐸−10	1.77772 𝐸−8	1.13695 𝐸−6	2.77022 𝐸−16
0.8	3.33067 𝐸−15	1.99840 𝐸−13	1.13132 𝐸−11	2.76944 𝐸−9	1.78208 𝐸−7	4.41936 𝐸−16
1	7.77156 𝐸−14	1.38778 𝐸−13	8.58313 𝐸−10	2.09593 𝐸−8	1.34244 𝐸−6	3.28504 𝑢𝑡𝑡=𝑢𝑥𝑥+𝑝(𝑢)𝑥𝑥+𝛼𝑢𝑥𝑥𝑥𝑥+𝛽𝑢𝑥𝑥𝑥𝑥𝑥𝑥,(6.20)