Recovery the interior temperature of a nonhomogeneous elliptic equation from boundary data

Journal of Inequalities and Applications

Table 1 Error estimations for the first regularization solution ( $δ^{1, ϵ}$ ) and the second regularization solution ( $δ^{2, ϵ}$ )

y	ϵ = 10⁻¹		ϵ = 10⁻³		ϵ = 10⁻⁵		ϵ = 10⁻⁷
y	$δ^{1, ϵ}$	$δ^{2, ϵ}$	$δ^{1, ϵ}$	$δ^{2, ϵ}$	$δ^{1, ϵ}$	$δ^{2, ϵ}$	$δ^{1, ϵ}$	$δ^{2, ϵ}$
0.0	$2.570 E - 01$	$1.035 E + 01$	$2.147 E - 01$	$1.903 E + 00$	$2.147 E - 01$	$2.987 E - 01$	$2.147 E - 01$	$2.158 E - 01$
0.1	$3.037 E + 00$	$1.080 E + 01$	$1.852 E + 00$	$2.321 E + 00$	$1.335 E + 00$	$3.359 E - 01$	$1.053 E + 00$	$1.964 E - 01$
0.2	$5.033 E + 00$	$1.101 E + 01$	$3.108 E + 00$	$2.799 E + 00$	$2.261 E + 00$	$4.275 E - 01$	$1.788 E + 00$	$1.825 E - 01$
0.3	$6.252 E + 00$	$1.098 E + 01$	$3.954 E + 00$	$3.289 E + 00$	$2.910 E + 00$	$5.756 E - 01$	$2.316 E + 00$	$1.902 E - 01$
0.4	$6.932 E + 00$	$1.075 E + 01$	$4.497 E + 00$	$3.751 E + 00$	$3.348 E + 00$	$7.574 E - 01$	$2.682 E + 00$	$2.319 E - 01$
0.5	$7.236 E + 00$	$1.037 E + 01$	$4.815 E + 00$	$4.156 E + 00$	$3.624 E + 00$	$4.868 E - 04$	$2.920 E + 00$	$2.954 E - 01$
0.6	$7.280 E + 00$	$9.873 E + 00$	$4.965 E + 00$	$4.483 E + 00$	$3.775 E + 00$	$9.559 E - 01$	$3.061 E + 00$	$3.703 E - 01$
0.7	$7.143 E + 00$	$9.308 E + 00$	$4.990 E + 00$	$4.725 E + 00$	$3.833 E + 00$	$1.359 E + 00$	$3.125 E + 00$	$4.508 E - 01$
0.8	$6.885 E + 00$	$8.702 E + 00$	$4.925 E + 00$	$4.877 E + 00$	$3.818 E + 00$	$1.548 E + 00$	$3.131 E + 00$	$5.327 E - 01$
0.9	$6.548 E + 00$	$8.082 E + 00$	$4.793 E + 00$	$4.943 E + 00$	$3.751 E + 00$	$1.721 E + 00$	$3.092 E + 00$	$6.135 E - 01$
1.0	$6.162 E + 00$	$7.464 E + 00$	$4.615 E + 00$	$4.930 E + 00$	$3.644 E + 00$	$1.874 E + 00$	$3.019 E + 00$	$6.910 E - 01$