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Theory and Modern Applications

Table 5 Numerical results with error analysis for Example 3

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 3 ( t )

F 1 , 3 ( t )

F 2 , 3 ( t )

F 3 , 3 ( t )

e 1 , 3 ( t ) , i = 1 , , 3

r = 1

10.500

−4.5000

1.7500

10.500

−4.5000

1.7500

0.0000

r = 2

9.2500

−4.8750

1.3125

9.2500

−4.8750

1.3125

0.0000

r = 3

8.6250

−4.9688

1.1406

8.6250

−4.9688

1.1406

0.0000

r = 4

8.3125

−4.9922

1.0664

8.3125

−4.9922

1.0664

0.0000

r = 5

8.1563

−4.9980

1.0322

8.1563

−4.9980

1.0322

0.0000

r = 6

8.0781

−4.9995

1.0159

8.0781

−4.9995

1.0159

0.0000

r = 7

8.0391

−4.9999

1.0079

8.0391

−4.9999

1.0079

0.0000

r = 8

8.0195

−5.0000

1.0039

8.0195

−5.0000

1.0039

0.0000

r = 9

8.0098

−5.0000

1.0020

8.0098

−5.0000

1.0020

0.0000