An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations

Table 3

The maximum error and root mean square error for problem (76).

	Method
1/2	Ref. [16]	2.6e − 4	6.5e − 5	1.6e − 5	4.1e − 6	1.0e − 6	2.6e − 7	6.4e − 8
	Our method; ()	2.34e − 4	6.37e − 5	1.65e − 5	4.20e − 6	1.06e − 6	2.72e − 7	5.21e − 8
1/4	Ref. [16]	1.9e − 3	4.7e − 4	1.2e − 4	2.9e − 5	7.4e − 6	1.8e − 6	4.6e − 7
	Our method; ()	3.04e − 3	8.19e − 4	2.11e − 4	5.38e − 5	1.35e − 5	3.36e − 6	1.94e − 7
1/8	Ref. [16]	7.3e − 2	1.9e − 2	4.7e − 3	1.2e − 3	2.9e − 4	7.3e − 5	1.8e − 5
	Our method; ()	8.23e − 2	2.39e − 2	6.13e − 3	1.54e − 3	3.93e − 4	9.66e − 5	6.74e − 7
1/16	Ref. [16]	2.9e − 2	7.1e − 3	1.8e − 3	4.4e − 4	1.1e − 4	2.8e − 5	6.9e − 6
	Our method; ()	1.61e − 2	4.03e − 3	1.04e − 3	2.67e − 4	6.80e − 5	1.66e − 5	3.74e − 6
1/32	Ref. [16]	—	3.8e—2	9.8e—3	2.5e—3	6.2e—4	1.5e—4	3.9e-5
	Our method; ()	7.52e − 2	1.99e − 2	5.06e − 3	1.30e − 3	3.25e − 4	7.93e − 5	1.12e − 5
1/64	Ref. [16]	—	3.4e − 2	8.7e − 3	2.2e − 3	5.5e − 4	1.4e − 4	3.4e − 5
	Our method; ()	8.54e − 2	2.33e − 2	6.39e − 3	1.63e − 3	4.10e − 4	1.03e − 4	1.85e − 5
1/128	Ref. [16]	—	—	2.8e − 2	7.2e − 3	1.8e − 3	4.5e − 4	1.1e − 4
	Our method; ()	—	6.46e − 2	1.69e − 2	4.33e − 3	1.09e − 3	2.73e − 4	5.70e − 5
1/256	Ref. [16]	—	—	—	—	6.3e − 2	1.6e − 2	3.9e − 3
	Our method; ()	—	—	—	—	3.21e − 2	8.09e − 3	9.13e − 4
1/512	Ref. [16]	—	—	—	—	4.2e − 2	1.0e − 2	2.5e − 3
	Our method; ()	—	—	—	—	2.12e − 2	5.35e − 3	6.92e − 4
1/1024	Ref. [16]	—	—	—	—	—	3.4e − 2	8.5e − 3
	Our method; ()	—	—	—	—	—	1.92e − 2	2.55e − 3