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

Table 1

For the case of 𝑎(𝑥)≠0, 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	0.02233220	0.01350608	0.00954256	0.00428337	0.00310038	0.00176533
	0.77	0.82	0.86	0.93	0.98	0.99
10^-4	0.02233215	0.01376835	0.00850615	0.00538213	0.00315446	0.00160520
	0.75	0.80	0.85	0.92	0.97	0.99
10^-6	0.02233210	0.01376065	0.00851454	0.00540203	0.00314356	0.00160544
	0.75	0.80	0.85	0.92	0.97	0.99
10^-8	0.02233205	0.01376074	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
10^-10	0.02233209	0.01376065	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
10^-12	0.02233209	0.01376065	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
10^-14	0.02233209	0.01376065	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
10^-16	0.02233213	0.01376074	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
10^-18	0.02233213	0.01376074	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
10^-20	0.02233213	0.01376074	0.00851405	0.00540203	0.00314356	0.00160522
	0.75	0.80	0.85	0.92	0.97	0.99
𝑒^𝑁	0.02233220	0.01376835	0.00954256	0.00540203	0.00315446	0.00176533
𝑝^𝑁	0.75	0.80	0.85	0.92	0.97	0.99