Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Error estimates and convergence rates for various N for Example 5.2

From: A high-order finite difference scheme for a singularly perturbed reaction-diffusion problem with an interior layer

Number of mesh points N
ε	64	128	256	512	1,024	2,048
10⁻²	5.5036e−3	4.3650e−4	2.1633e−5	1.1995e−6	7.0962e−8	4.2920e−9
10⁻²	4.702	5.369	5.027	4.811	4.693	-
10⁻³	9.0903e−3	1.7499e−3	1.9075e−4	1.6259e−5	1.4964e−6	1.4532e−7
10⁻³	3.057	3.960	4.280	4.059	3.901	-
10⁻⁴	9.0667e−3	1.7458e−3	1.9024e−4	1.6213e−5	1.5079e−6	1.4493e−7
10⁻⁴	3.057	3.961	4.280	4.041	3.918	-
10⁻⁵	9.0644e−3	1.7454e−3	1.9019e−4	1.6208e−5	1.5091e−6	1.4489e−7
10⁻⁵	3.056	3.961	4.280	4.039	3.920	-
10⁻⁶	9.0641e−3	1.7453e−3	1.9018e−4	1.6208e−5	1.5092e−6	1.4489e−7
10⁻⁶	3.056	3.961	4.280	4.039	3.920	-
10⁻⁷	9.0641e−3	1.7453e−3	1.9018e−4	1.6208e−5	1.5092e−6	1.4491e−7
10⁻⁷	3.056	3.961	4.280	4.039	3.920	-
10⁻⁸	9.0641e−3	1.7453e−3	1.9018e−4	1.6208e−5	1.5092e−6	1.4507e−7
10⁻⁸	3.056	3.961	4.280	4.039	3.918	-
10⁻⁹	9.0641e−3	1.7453e−3	1.9018e−4	1.6209e−5	1.5092e−6	1.4666e−7
10⁻⁹	3.056	3.961	4.280	4.039	3.899	-
\(E^{N}\)	9.0903e−3	1.7499e−3	1.9075e−4	1.6259e−5	1.5092e−6	1.4666e−7
\(R^{N}\)	3.057	3.960	4.280	4.044	3.899	-

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