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Theory and Modern Applications

Table 5 Comparison of numerical results of Example 5.1 with Shishkin mesh with \(\varepsilon _{2}=10^{-2}\)

From: Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations

N/Δt

\(\varepsilon _{1}=10^{-4}\)

\(\varepsilon _{1}=10^{-6}\)

Shishkin mesh

Adaptive mesh

Shishkin mesh

Adaptive mesh

\(32/\frac{1}{20}\)

4.8924e − 01

1.6708e − 01

4.9039e − 01

1.7981e − 01

0.0917

0.7887

0.0920

0.8831

\(64/\frac{1}{40}\)

4.5911e − 01

9.6715e − 02

4.6011e − 01

9.7493e − 02

0.0354

0.8874

0.0357

0.8709

\(128/\frac{1}{80}\)

4.4799e − 01

5.2283e − 02

4.4885e − 01

5.3310e − 02

0.0151

0.9177

0.0154

0.9153

\(256/\frac{1}{160}\)

4.4334e − 01

2.7677e − 02

4.4409e − 01

2.8267e − 02