The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions

Table 1

The numerical results for Example 1.

Node	True solution 𝑢(𝑥)	Approximate solution 𝑢100(𝑥)	Absolute error	Relative error
0.1	2.57757	2.57756	1.39670E − 5	5.41865E − 6
0.2	3.85257	3.85255	2.08943E − 5	5.42347E − 6
0.3	4.78900	4.78897	2.59723E − 5	5.42333E − 6
0.4	5.36114	5.36111	2.90522E − 5	5.41903E − 6
0.5	5.55357	5.55354	3.00501E − 5	5.41096E − 6
0.6	5.36114	5.36111	2.89504E − 5	5.40005E − 6
0.7	4.78900	4.78897	2.58036E − 5	5.38810E − 6
0.8	3.85257	3.85255	2.07194E − 5	5.37806E − 6
0.9	2.57757	2.57756	1.38544E − 5	5.37499E − 6
1.0	1	0.999995	5.39775E − 6	5.39775E − 6