From: A pertinent approach to solve nonlinear fuzzy integro-differential equations
\(\alpha\) | Exact solution | Approximate solution | Error | |||
---|---|---|---|---|---|---|
\({\underline{u}} \left( {x,\alpha } \right)\) | \(\bar{u}\left( {x, \alpha } \right)\) | \({\underline{u}} \left( {x,\alpha } \right)\) | \(\bar{u}\left( {x, \alpha } \right)\) | \({\underline{E}} \left( {x,\alpha } \right)\) | \(\bar{E}\left( {x,\alpha } \right)\) | |
0 | 0 | 3.297440 | 0 | 3.297412 | 0 | 0.000028 |
0.1 | 0.164872 | 3.132570 | 0.164718 | 3.132432 | 0.000154 | 0.000138 |
0.2 | 0.329744 | 2.967699 | 0.329726 | 2.967489 | 0.000018 | 0.000210 |
0.3 | 0.494616 | 2.802826 | 0.494592 | 2.802652 | 0.000024 | 0.000174 |
0.4 | 0.659489 | 2.637954 | 0.659456 | 2.637726 | 0.000033 | 0.000228 |
0.5 | 0.824631 | 2.473082 | 0.824586 | 2.472886 | 0.000045 | 0.000916 |
0.6 | 0.989233 | 2.308210 | 0.989196 | 2.307985 | 0.000037 | 0.000225 |
0.7 | 1.154100 | 2.143338 | 1.154069 | 2.143228 | 0.000031 | 0.000011 |
0.8 | 1.318980 | 1.978466 | 1.318952 | 1.978395 | 0.000028 | 0.000071 |
0.9 | 1.483850 | 1.813593 | 1.483808 | 1.813587 | 0.000042 | 0.000006 |
1 | 1.648720 | 1.648721 | 1.648672 | 1.648706 | 0.000048 | 0.000015 |