An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

Table 6

Comparison of the second-order approximate solution with exact solution.

𝑥	𝑈𝐸	𝑈2	Error
0	0.0000000000	0.0000000000	0.000𝐸 + 000
0.1	0.0198100000	0.0198100068	6.800𝐸−009
0.2	0.0771200000	0.0771200239	2.390𝐸−008
0.3	0.1662300000	0.1662300464	4.640𝐸−008
0.4	0.2790400000	0.2790400692	6.920𝐸−008
0.5	0.4062500000	0.4062500874	8.740𝐸−008
0.6	0.5385600000	0.5385600961	9.610𝐸−008
0.7	0.6678700000	0.6678700906	9.060𝐸−008
0.8	0.7884800000	0.7884800670	6.700𝐸−008
0.9	0.8982900000	0.8982900292	2.920𝐸−008
1.0	1.0000000000	1.0000000012	1.200𝐸−009