Table 1 Error estimate between the exact solution and its regularized solution for the a priori parameter and the a posteriori parameter choice rules in Example 1
From: On an inverse problem in the parabolic equation arising from groundwater pollution problem
ϵ | \(\boldsymbol{E_{1}^{\mu_{1}}}\) | \(\boldsymbol{E_{2}^{\mu_{1}}}\) | \(\boldsymbol{E_{1}^{\mu _{2}}}\) | \(\boldsymbol{E_{2}^{\mu_{2}}}\) |
|---|---|---|---|---|
5.0E − 01 | 2.19973047E − 01 | 6.25280883E − 01 | 2.37722314E − 01 | 6.75733186E − 01 |
1.0E − 01 | 4.84352308E − 02 | 1.37678794E − 01 | 5.74458438E − 02 | 1.63291769E − 01 |
5.0E − 02 | 2.61788488E − 02 | 7.44142701E − 02 | 2.83719452E − 02 | 8.06482211E − 02 |
1.0E − 02 | 8.18020277E − 03 | 2.32525051E − 02 | 8.06299020E − 03 | 2.29193244E − 02 |
5.0E − 03 | 5.77361943E − 03 | 1.64117100E − 02 | 5.73993055E − 03 | 1.63159482E − 02 |
1.0E − 03 | 4.80971954E − 03 | 1.36717917E − 02 | 4.54649392E − 03 | 1.29235639E − 02 |
5.0E − 04 | 4.67487514E − 03 | 1.32884919E − 02 | 4.54039711E − 03 | 1.29062335E − 02 |
1.0E − 04 | 4.48497982E − 03 | 1.27487080E − 02 | 4.41615901E − 03 | 1.25530824E − 02 |
5.0E − 05 | 4.44987772E − 03 | 1.26489290E − 02 | 4.41003343E − 03 | 1.25356703E − 02 |
1.0E − 05 | 4.41942400E − 03 | 1.25623633E − 02 | 4.40598999E − 03 | 1.25241767E − 02 |