Research Article
Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions
Table 3
Numerical values and absolute error values by using TMM and PNM,
, at linear case
.
| | | | | TMM | PNM | | | | |
| 0.01 | -1.0 | -1.0 | 1.0000 | 1.00037 | 0.000378 | 1.00067 | 0.000673 | -0.8 | -0.8 | 0.6400 | 0.64077 | 0.000775 | 0.64067 | 0.000673 | -0.6 | -0.6 | 0.3600 | 0.36077 | 0.000772 | 0.36067 | 0.000742 | -0.4 | -0.4 | 0.1600 | 0.16076 | 0.000768 | 0.16067 | 0.000672 | -0.2 | -0.2 | 0.0400 | 0.04074 | 0.000747 | 0.04067 | 0.000674 | 0 | 0 | 0.0000 | 0.00116 | 0.001160 | 0.00067 | 0.000674 | 0.2 | 0.2 | 0.0400 | 0.04074 | 0.000747 | 0.04067 | 0.000674 | 0.4 | 0.4 | 0.1600 | 0.16076 | 0.000768 | 0.16067 | 0.000674 | 0.6 | 0.6 | 0.3600 | 0.36077 | 0.000772 | 0.36067 | 0.000674 | 0.8 | 0.8 | 0.6400 | 0.64077 | 0.000775 | 0.64067 | 0.000749 | 1.0 | 1.0 | 1.0000 | 1.00037 | 0.000378 | 1.00067 | 0.000675 |
| 0.001 | -1.0 | -1.0 | 1.0000 | 1.00003 | 0.000037 | 1.00006 | 0.000067 | -0.8 | -0.8 | 0.6400 | 0.64007 | 0.000077 | 0.64006 | 0.000067 | -0.6 | -0.6 | 0.3600 | 0.36007 | 0.000077 | 0.36006 | 0.000067 | -0.4 | -0.4 | 0.1600 | 0.16007 | 0.000076 | 0.16006 | 0.000067 | -0.2 | -0.2 | 0.0400 | 0.04007 | 0.000074 | 0.04006 | 0.000067 | 0 | 0 | 0.0000 | 0.00011 | 0.000115 | 0.00006 | 0.000067 | 0.2 | 0.2 | 0.0400 | 0.04007 | 0.000074 | 0.04006 | 0.000067 | 0.4 | 0.4 | 0.1600 | 0.16007 | 0.000076 | 0.16006 | 0.000067 | 0.6 | 0.6 | 0.3600 | 0.36007 | 0.000077 | 0.36006 | 0.000067 | 0.8 | 0.8 | 0.6400 | 0.64007 | 0.000077 | 0.64006 | 0.000067 | 1.0 | 1.0 | 1.0000 | 1.00003 | 0.000037 | 1.00006 | 0.000067 |
|
|