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Theory and Modern Applications

Table 1 Errors \(e_{u}^{ \varepsilon,N}\) computed ε-uniform errors \(e_{u}^{N}\) and convergence rates \(p_{u}^{ \varepsilon,N}\) on \(\omega_{N}\)

From: A parameter uniform difference scheme for the parameterized singularly perturbed problem with integral boundary condition

ε

N = 64

N = 128

N = 256

N = 512

N = 1024

20

0.00464342

0.00249526

0.00128984

0.00065893

0.00033245

0.896

0.952

0.969

0.987

 

2−4

0.00692191

0.00372224

0.00192142

0.00065782

0.00033143

0.895

0.954

0.974

0.989

 

2−8

0.00460314

0.00247876

0.00128398

0.00065412

0.00032979

0.893

0.949

0.973

0.988

 

2−12

0.00460181

0.00247290

0.00128183

0.00065348

0.00032947

0.896

0.948

0.972

0.988

 

2−16

0.00460557

0.00247492

0.00128110

0.00065175

0.00032837

0.896

0.950

0.975

0.989

 

\(e_{u}^{\varepsilon,N}\)

0.00464342

0.00372224

0.00128984

0.00065893

0.00033245

\(p_{u}^{\varepsilon,N}\)

0.895

0.954

0.969

0.987

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