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Theory and Modern Applications

Table 1 Approximate errors e N and computed orders of convergence p N on ω ¯ N for various values of ε and N

From: Numerical solution of a singularly perturbed Volterra integro-differential equation

ε

N = 16

N = 32

N = 64

N = 128

N = 256

N = 512

10−1

0.048432

0.025428

0.013244

0.006847

0.003533

0.001797

0.93

0.94

0.95

0.95

0.97

 

10−2

0.049452

0.015768

0.013189

0.006691

0.003367

0.001691

0.94

0.97

0.98

0.99

0.99

 

10−3

0.050015

0.026007

0.013277

0.006723

0.003381

0.001697

0.94

0.97

0.98

0.99

0.99

 

10−4

0.050137

0.026058

0.013295

0.006730

0.003384

0.001698

0.94

0.97

0.98

0.99

0.99

 

10−5

0.050146

0.026062

0.013297

0.006733

0.003385

0.001698

0.94

0.97

0.98

0.99

0.99

 

10−6

0.050149

0.026063

0.013297

0.006734

0.003385

0.001698

0.94

0.97

0.98

0.99

0.99