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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Numerical results with error analysis for Example 2

$t = \frac{1}{2^{r}}$	Exact solution		Approximate solution		Error
$t = \frac{1}{2^{r}}$	$F_{1} (t)$	$F_{2} (t)$	$F_{1, 4} (t)$	$F_{2, 4} (t)$	$e_{1, 4} (t)$	$e_{2, 4} (t)$
r = 1	0.4794	1.6487	0.4795	1.6488	0.0001	0.0001
r = 2	0.2474	1.2840	0.2472	1.2825	0.0002	0.0016
r = 3	0.1247	1.1331	0.1244	1.1315	0.0003	0.0016
r = 4	0.0625	1.0645	0.0622	1.0634	0.0002	0.0011
r = 5	0.0312	1.0317	0.0311	1.0311	0.0001	0.0006
r = 6	0.0156	1.0157	0.0156	1.0154	0.0001	0.0003
r = 7	0.0078	1.0078	0.0078	1.0077	0.0001	0.0002
r = 8	0.0039	1.0039	0.0039	1.0038	0.0001	0.0001
r = 9	0.0020	1.0020	0.0019	1.0019	0.0001	0.0001