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Table 4 The numerical results for Example 4 with \({x}=0.5\), \({M} =2\), \({N} =3\)

From: Study of hybrid orthonormal functions method for solving second kind fuzzy Fredholm integral equations

r Exact solution \(( \underline{u} ( x,r ), \overline{u} ( x,r ) )\) Presented method Absolute error
0 (0.00000,0.50000) (0.00000,1.00000) (3.98881e − 12,4.90985e − 12)
0.1 (0.02500,0.47500) (0.05000,0.95000) (3.11232e − 12,3.77101e − 12)
0.2 (0.05000,0.45000) (0.10000,0.90000) (2.34518e − 12,2.77027e − 12)
0.3 (0.07500,0.42500) (0.15000,0.85000) (1.68740e − 12,1.90765e − 12)
0.4 (0.10000,0.40000) (0.20000,0.80000) (1.13896e − 12,1.18320e − 12)
0.5 (0.12500,0.37500) (0.25000,0.75000) (7.67386e − 13,0.00000e + 00)
0.6 (0.15000,0.35000) (0.30000,0.70000) (4.40253e − 13,1.54612e − 12)
0.7 (0.17500,0.32500) (0.35000,0.65000) (2.20562e − 13,3.09229e − 12)
0.8 (0.20000,0.30000) (0.40000,0.60000) (1.08286e − 13,4.63841e − 12)
0.9 (0.22500,0.27500) (0.45000,0.55000) (1.13459e − 12,1.43827e − 10)