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Theory and Modern Applications

Table 4 Rate of convergence \(r_{\varepsilon _{1},\varepsilon _{2}} ^{N,M}\) for Example 5.1 using the adaptive grid method with \(\varepsilon _{2}=10^{-2}\)

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

\(\varepsilon _{1}\)

Number of intervals N/time size Δt

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

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

\(128/\frac{1}{60}\)

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

10−3

0.7874

0.8749

0.9457

0.9651

10−4

0.7887

0.8874

0.9177

0.9577

10−5

0.8883

0.8791

0.9065

0.8905

10−6

0.8831

0.8709

0.9153

0.7581

10−7

0.8356

0.9118

0.8950

0.7664