Research Article
Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments
Table 3
Numerical solution of Example
2 for different
values.
| Present method and corrected Laguerre polynomial solution | | Exact solution | | | | | | |
| 0.0 | 4.000000 | 4.000000 | 4.000000 | 3.999999 | 3.999999 | 4.000000 | 4.000000 | 0.1 | 3.610000 | 3.607781 | 3.608978 | 3.607685 | 3.610898 | 3.610363 | 3.608798 | 0.2 | 3.240000 | 3.230410 | 3.235483 | 3.230156 | 3.243601 | 3.240185 | 3.235706 | 0.3 | 2.890000 | 2.867005 | 2.878938 | 2.866678 | 2.898090 | 2.887697 | 2.881383 | 0.4 | 2.560000 | 2.516891 | 2.538843 | 2.516663 | 2.574315 | 2.551308 | 2.546356 | 0.5 | 2.250000 | 2.179554 | 2.214765 | 2.179633 | 2.272214 | 2.229593 | 2.231063 | 0.6 | 1.960000 | 1.854596 | 1.906326 | 1.855192 | 1.991717 | 1.921284 | 1.935850 | 0.7 | 1.690000 | 1.541700 | 1.613200 | 1.543010 | 1.732756 | 1.625252 | 1.661011 | 0.8 | 1.440000 | 1.240609 | 1.335103 | 1.242812 | 1.495265 | 1.340495 | 1.406788 | 0.9 | 1.210000 | 0.951112 | 1.071789 | 0.954366 | 1.279181 | 1.066119 | 1.173387 | 1.0 | 1.000000 | 0.673025 | 0.823042 | 0.677475 | 1.084448 | 0.801327 | 0.960984 |
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