Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

Table 1

Relative error for different values of parameter 𝐻 for Example 1.

𝑋	𝐻=0	𝐻=0.5	𝐻=1	𝐻=2	𝐻=3	𝐻=5	𝐻=10
	𝑁=10	𝑁=10	𝑁=10	𝑁=20	𝑁=20	𝑁=30	𝑁=40
0.0	0	0	0	0	0	0	0
0.1	1.0000𝐸−10	5.963𝐸−11	2.708𝐸−9	5.1850𝐸−9	3.6328𝐸−8	8.9622𝐸−8	9.0871𝐸−7
0.2	1.0000𝐸−10	1.145𝐸−10	5.337𝐸−9	1.0504𝐸−8	7.3297𝐸−8	1.7941𝐸−7	1.8174𝐸−6
0.3	1.0000𝐸−10	1.640𝐸−10	7.842𝐸−9	1.5952𝐸−8	1.1120𝐸−7	2.6957𝐸−7	2.7261𝐸−6
0.4	1.0000𝐸−10	2.079𝐸−10	1.017𝐸−8	2.1492𝐸−8	1.5038𝐸−7	3.6059𝐸−7	3.6349𝐸−6
0.5	1.0000𝐸−10	2.457𝐸−10	1.229𝐸−8	2.7024𝐸−8	1.9106𝐸−7	4.5343𝐸−7	4.5440𝐸−6
0.6	1.0000𝐸−10	2.773𝐸−10	1.413𝐸−8	3.2361𝐸−8	2.3301𝐸−7	5.4982𝐸−7	5.4547𝐸−6
0.7	1.0000𝐸−10	3.020𝐸−10	1.561𝐸−8	3.7203𝐸−8	2.7477𝐸−7	6.5192𝐸−7	6.3745𝐸−6
0.8	1.0000𝐸−10	3.199𝐸−10	1.673𝐸−8	4.1147𝐸−8	3.1262𝐸−7	7.5863𝐸−7	7.3351𝐸−6
0.9	1.0000𝐸−10	3.307𝐸−10	1.741𝐸−8	4.3753𝐸−8	3.4019𝐸−7	8.5360𝐸−7	8.3951𝐸−6
1.0	1.0000𝐸−10	3.344𝐸−10	1.766𝐸−8	4.4668𝐸−8	3.5045𝐸−7	4.2434𝐸−7	9.0872𝐸−6