A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

Table 2

For the case 𝑎(0)=0 of approximate errors 𝑒^𝑁_𝜀 and 𝑒^𝑁 and the computed orders of convergence 𝑝^𝑁_𝜀 on the piecewise uniform mesh 𝜔_𝑁 for various values of 𝜀 and 𝑁.

𝜀	𝑁=8	𝑁=16	𝑁=32	𝑁=64	𝑁=128	𝑁=256
10^-2	0.02453225	0.01721110	0.01123085	0.00652485	0.00439674	0.00189543
	0.68	0.79	0.83	0.88	0.96	0.99
10^-4	0.02453220	0.01716585	0.01120973	0.00651194	0.00439686	0.00188515
	0.67	0.76	0.80	0.85	0.94	0.99
10^-6	0.02453221	0.01706582	0.01120403	0.00651089	0.0043 9225	0.00188523
	0.67	0.76	0.80	0.85	0.94	0.99
10^-8	0.02453215	0.01706553	0.01120282	0.00651046	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
10^-10	0.02453215	0.01706593	0.01120275	0.00651093	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
10^-12	0.02453216	0.01706452	0.01120270	0.00651025	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
10^-14	0.02453209	0.01706425	0.01120256	0.00651025	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
10^-16	0.02453209	0.01706425	0.01120256	0.00651025	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
10^-18	0.02453209	0.01706425	0.01120256	0.00651025	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
10^-20	0.02453209	0.01706425	0.01120256	0.00651025	0.00439214	0.00188517
	0.67	0.76	0.80	0.85	0.94	0.99
𝑒^𝑁	0.02453225	0.01716585	0.01123085	0.00652485	0.00439686	0.00189543
𝑝^𝑁	0.68	0.79	0.83	0.88	0.96	0.99