Research Article
Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions
Table 1
Numerical values and absolute error values by using TMM and PNM,
, at linear case
.
| | | | | TMM | PNM | | | | |
| 0.01 | -1.0 | -1.0 | 1.0000 | 0.99120 | 0.008797 | 0.98999 | 0.010000 | -0.8 | -0.8 | 0.6400 | 0.62784 | 0.012154 | 0.62790 | 0.012094 | -0.6 | -0.6 | 0.3600 | 0.35051 | 0.009489 | 0.34924 | 0.010750 | -0.4 | -0.4 | 0.1600 | 0.15502 | 0.004974 | 0.15224 | 0.007754 | -0.2 | -0.2 | 0.0400 | 0.03874 | 0.001256 | 0.03590 | 0.004092 | 0 | 0 | 0.0000 | 0.00229 | 0.000229 | 0.00006 | 0.000060 | 0.2 | 0.2 | 0.0400 | 0.03874 | 0.001256 | 0.43951 | 0.003951 | 0.4 | 0.4 | 0.1600 | 0.15502 | 0.004974 | 0.16759 | 0.007599 | 0.6 | 0.6 | 0.3600 | 0.35051 | 0.009489 | 0.37048 | 0.010488 | 0.8 | 0.8 | 0.6400 | 0.62784 | 0.012154 | 0.65197 | 0.011978 | 1.0 | 1.0 | 1.0000 | 0.99120 | 0.008797 | 1.00991 | 0.009916 |
| 0.001 | -1.0 | -1.0 | 1.0000 | 0.99912 | 0.000878 | 0.99899 | 0.001001 | -0.8 | -0.8 | 0.6400 | 0.63879 | 0.001212 | 0.63879 | 0.001209 | -0.6 | -0.6 | 0.3600 | 0.35905 | 0.000945 | 0.35892 | 0.001076 | -0.4 | -0.4 | 0.1600 | 0.15950 | 0.000495 | 0.15922 | 0.000776 | -0.2 | -0.2 | 0.0400 | 0.03987 | 0.000124 | 0.03958 | 0.000411 | 0 | 0 | 0.0000 | 0.00002 | 0.000023 | | | 0.2 | 0.2 | 0.0400 | 0.03987 | 0.000124 | 0.04039 | 0.000393 | 0.4 | 0.4 | 0.1600 | 0.15950 | 0.000495 | 0.16075 | 0.000759 | 0.6 | 0.6 | 0.3600 | 0.35905 | 0.000945 | 0.36104 | 0.001048 | 0.8 | 0.8 | 0.6400 | 0.63878 | 0.001212 | 0.64119 | 0.001197 | 1.0 | 1.0 | 1.0000 | 0.99912 | 0.000878 | 1.00099 | 0.000991 |
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