The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method

Table 1

The absolute error of Example 3.1.

Absolute error
𝑥	Present (𝑛=20)	Present (𝑛=40)	Present (𝑛=80)	Present (𝑛=160)	Ref. [3]	Ref. [2]	Present (𝑛=500)
0.0	0	0	0	0	0	0	0
0.1	1.52298×10^−5	2.85196×10^−6	5.80026×10^−7	1.27547×10^−7	1×10^−7	0	1.18126×10^−8
0.3	7.42332×10^−5	1.5986×10^−5	3.66544×10^−6	8.74382×10^−7	3×10^−7	5×10^−3	8.65902×10^−8
0.4	1.08810×10^−4	2.42167×10^−5	5.67330×10^−6	1.37023×10^−6	5×10^−7	7×10^−3	1.36944×10^−7
0.5	1.40256×10^−4	3.19274×10^−5	7.58382×10^−6	1.84582×10^−6	6×10^−7	8×10^−3	1.85506×10^−7
0.7	1.68693×10^−4	3.95170×10^−5	9.54427×10^−6	2.3440×10^−6	7×10^−7	7×10^−3	2.37089×10^−7
0.9	9.78854×10^−5	2.33293×10^−5	5.68883×10^−6	1.40422×10^−6	4×10^−7	4×10^−3	1.42538×10^−7
1.0	1.50887×10^−15	1.74768×10^−15	1.57219×10^−15	1.90655×10^−15	0	1.4×10^−2	1.49019×10^−15
	0 s < CPU runtime ≤ 1 s		CPU runtime ≤ 10 s				CPU runtime = 180 s