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