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Theory and Modern Applications

Table 1 Numerical results with error analysis for Example 1

From: Numerical solution of linear integral equations system using the Bernstein collocation method

t= 1 2 r

Exact solution

Approximate solution

Error

F 1 ( t )

F 2 ( t )

F 1 , 3 ( t )

F 2 , 3 ( t )

e 1 , 3 ( t )

e 2 , 3 ( t )

r = 1

1.6487

0.6667

1.6484

0.6658

0.0004

0.0009

r = 2

1.2840

0.5714

1.2845

0.5724

0.0004

0.0010

r = 3

1.1331

0.5333

1.1339

0.5350

0.0008

0.0016

r = 4

1.0645

0.5161

1.0650

0.5174

0.0005

0.0012

r = 5

1.0317

0.5079

1.0320

0.5087

0.0003

0.0008

r = 6

1.0157

0.5039

1.0159

0.5044

0.0001

0.0005

r = 7

1.0078

0.5020

1.0079

0.5023

0.0001

0.0003

r = 8

1.0039

0.5010

1.0039

0.5012

0.0000

0.0002

r = 9

1.0020

0.5005

1.0019

0.5007

0.0001

0.0002