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Table 3 The numerical results for Example 3 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 (0.00000,1.00000) (0.00000,1.00000) (1.11378e − 11,9.60654e − 12)
0.1 (0.05000,0.95000) (0.05000,0.95000) (8.82267e − 12,7.71254e − 12)
0.2 (0.10000,0.90000) (0.10000,0.90000) (6.79151e − 12,5.94123e − 12)
0.3 (0.15000,0.85000) (0.15000,0.85000) (5.04428e − 12,4.29281e − 12)
0.4 (0.20000,0.80000) (0.20000,0.80000) (3.58099e − 12,2.76719e − 12)
0.5 (0.25000,0.75000) (0.25000,0.75000) (1.53477e − 12,0.00000e + 00)
0.6 (0.30000,0.70000) (0.30000,0.70000) (8.80507e − 13,3.09224e − 12)
0.7 (0.35000,0.65000) (0.35000,0.65000) (4.41125e − 13,6.18459e − 12)
0.8 (0.40000,0.60000) (0.40000,0.60000) (2.16571e − 13,9.27682e − 12)
0.9 (0.45000,0.55000) (0.45000,0.55000) (1.80808e − 11,1.17943e − 10)