Research Article
Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions
Table 4
Numerical values and absolute error values by using TMM and PNM,
, at nonlinear case
.
| | | | | TMM | PNM | | | | |
| 0.01 | -1.0 | -1.0 | 1.0000 | 0.995933 | 0.004066 | 0.996224 | 0.003775 | -0.8 | -0.8 | 0.6400 | 0.636315 | 0.003684 | 0.636219 | 0.00378 | -0.6 | -0.6 | 0.3600 | 0.356318 | 0.003681 | 0.356222 | 0.003777 | -0.4 | -0.4 | 0.1600 | 0.156321 | 0.003678 | 0.156226 | 0.003773 | -0.2 | -0.2 | 0.0400 | 0.036307 | 0.003692 | 0.036229 | 0.003770 | 0 | 0 | 0.0000 | 0.003283 | 0.003283 | 0.003769 | 0.003769 | 0.2 | 0.2 | 0.0400 | 0.036307 | 0.003692 | 0.036299 | 0.003770 | 0.4 | 0.4 | 0.1600 | 0.156321 | 0.003678 | 0.156226 | 0.003777 | 0.6 | 0.6 | 0.3600 | 0.356318 | 0.003681 | 0.356222 | 0.003777 | 0.8 | 0.8 | 0.6400 | 0.636315 | 0.003684 | 0.636220 | 0.000377 | 1.0 | 1.0 | 1.0000 | 0.995933 | 0.004066 | 0.996226 | 0.003777 |
| 0.001 | -1.0 | -1.0 | 1.0000 | 0.999593 | 0.000403 | 0.999623 | 0.000376 | -0.8 | -0.8 | 0.6400 | 0.639632 | 0.000367 | 0.639622 | 0.000377 | -0.6 | -0.6 | 0.3600 | 0.359632 | 0.000367 | 0.359622 | 0.000377 | -0.4 | -0.4 | 0.1600 | 0.159632 | 0.000367 | 0.159623 | 0.000376 | -0.2 | -0.2 | 0.0400 | 0.039631 | 0.000368 | 0.396236 | 0.000376 | 0 | 0 | 0.0000 | 0.000327 | 0.000327 | 0.000376 | 0.000376 | 0.2 | 0.2 | 0.0400 | 0.039631 | 0.000368 | 0.039623 | 0.000376 | 0.4 | 0.4 | 0.1600 | 0.159632 | 0.000367 | 0.159623 | 0.000376 | 0.6 | 0.6 | 0.3600 | 0.359632 | 0.000367 | 0.359622 | 0.000377 | 0.8 | 0.8 | 0.6400 | 0.639322 | 0.000367 | 0.639622 | 0.000377 | 1.0 | 1.0 | 1.0000 | 0.999593 | 0.000406 | 0.999623 | 0.000376 |
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