Table 2 Error estimation between the exact solution and its regularized solution for both the a priori parameter choice rule and the a posteriori parameter choice rule in Example 2
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 | 8.73911561E + 01 | 6.23557272E − 01 | 1.68095756E + 02 | 1.19940433E + 00 |
1.0E − 01 | 1.73478908E + 01 | 1.23781444E − 01 | 1.68873801E + 01 | 1.20495587E − 01 |
5.0E − 02 | 9.04295359E + 00 | 6.45236855E − 02 | 1.05889724E + 01 | 7.55549079E − 02 |
1.0E − 02 | 2.51478744E + 00 | 1.79436234E − 02 | 1.77559899E + 00 | 1.26693331E − 02 |
5.0E − 03 | 1.33146975E + 00 | 9.50036234E − 03 | 7.94414569E − 01 | 5.66834224E − 03 |
1.0E − 03 | 4.04066751E − 01 | 2.88311509E − 03 | 1.79227628E − 01 | 1.27883296E − 03 |
5.0E − 04 | 2.24155836E − 01 | 1.59940671E − 03 | 8.74185405E − 02 | 6.23752667E − 04 |
1.0E − 04 | 7.42023262E − 02 | 5.29451745E − 04 | 1.85142488E − 02 | 1.32103693E − 04 |
5.0E − 05 | 4.58148569E − 02 | 3.26900209E − 04 | 9.69012336E − 03 | 6.66814607E − 05 |
1.0E − 05 | 1.56186641E − 02 | 1.11442988E − 04 | 1.86120018E − 03 | 1.32801185E − 05 |