Research Article
Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions
Table 2
Numerical values and absolute error values by using TMM and PNM,
, at nonlinear case
.
| | | | | TMM | PNM | | | | |
| 0.01 | -1.0 | -1.0 | 1.0000 | 0.99939 | 0.000605 | 0.998146 | 0.0018535 | -0.8 | -0.8 | 0.6400 | 0.63839 | 0.001604 | 0.637179 | 0.0028200 | -0.6 | -0.6 | 0.3600 | 0.35881 | 0.001182 | 0.357505 | 0.0024945 | -0.4 | -0.4 | 0.1600 | 0.15939 | 0.000605 | 0.158220 | 0.0017792 | -0.2 | -0.2 | 0.0400 | 0.03962 | 0.000375 | 0.038720 | 0.0012790 | 0 | 0 | 0.0000 | 0.00026 | 0.000260 | 0.001018 | 0.0010188 | 0.2 | 0.2 | 0.0400 | 0.03962 | 0.000375 | 0.038870 | 0.0011290 | 0.4 | 0.4 | 0.1600 | 0.15939 | 0.000605 | 0.158457 | 0.0015420 | 0.6 | 0.6 | 0.3600 | 0.35881 | 0.001182 | 0.357663 | 0.0021336 | 0.8 | 0.8 | 0.6400 | 0.63839 | 0.001604 | 0.637399 | 0.0026000 | 1.0 | 1.0 | 1.0000 | 0.99939 | 0.000605 | 0.999817 | 0.0019020 |
| 0.001 | -1.0 | -1.0 | 1.0000 | 0.99993 | 0.000060 | 0.639719 | 0.0001821 | -0.8 | -0.8 | 0.6400 | 0.63989 | 0.000160 | 0.159821 | 0.0002809 | -0.6 | -0.6 | 0.3600 | 0.35988 | 0.000117 | 0.359747 | 0.0002527 | -0.4 | -0.4 | 0.1600 | 0.15993 | 0.000060 | 0.359821 | 0.0001780 | -0.2 | -0.2 | 0.0400 | 0.03996 | 0.000037 | 0.039871 | 0.0001280 | 0 | 0 | 0.0000 | 0.000025 | 0.000025 | 0.000102 | 0.0001021 | 0.2 | 0.2 | 0.0400 | 0.039962 | 0.000037 | 0.039887 | 0.0001122 | 0.4 | 0.4 | 0.1600 | 0.159939 | 0.000060 | 0.159845 | 0.0001542 | 0.6 | 0.6 | 0.3600 | 0.359882 | 0.000117 | 0.359786 | 0.0002133 | 0.8 | 0.8 | 0.6400 | 0.639839 | 0.000160 | 0.639739 | 0.0002600 | 1.0 | 1.0 | 1.0000 | 0.999939 | 0.000060 | 0.999809 | 0.0001902 |
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