A pertinent approach to solve nonlinear fuzzy integro-differential equations

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Table 1 Comparisons between exact and approximate solutions at x = 0.5

\(\alpha\)	Exact solution		Approximate solution		Error
\(\alpha\)	\({\underline{u}} \left( {x,\alpha } \right)\)	\(\bar{u}\left( {x, \alpha } \right)\)	\({\underline{u}} \left( {x,\alpha } \right)\)	\(\bar{u}\left( {x, \alpha } \right)\)	\({\underline{E}} \left( {x,\alpha } \right)\)	\(\bar{E}\left( {x,\alpha } \right)\)
0	0	1	0	0.985254	0	0.014746
0.1	0.050000	0.950000	0.048711	0.943658	0.001289	0.006342
0.2	0.100000	0.900000	0.097247	0.896235	0.002753	0.003765
0.3	0.150000	0.850000	0.146107	0.848632	0.003893	0.003680
0.4	0.200000	0.800000	0.197524	0.792325	0.002476	0.007675
0.5	0.250000	0.750000	0.249120	0.749856	0.000880	0.000144
0.6	0.300000	0.700000	0.299771	0.699762	0.000229	0.000238
0.7	0.350000	0.650000	0.3496260	0.649823	0.000374	0.000177
0.8	0.400000	0.600000	0.399712	0.599735	0.000288	0.000265
0.9	0.450000	0.550000	0.449252	0.549753	0.000748	0.000247
1	0.500000	0.500000	0.499783	0.499685	0.000217	0.000315