Table 2 Comparing of numerical solutions/REFs using QLM-FSVLFs technique for \(\gamma =2,\sigma =1\), \(\lambda ,m=1\), \(K=8\), and various \(r\in [0,1]\).
r | QLM-FSVLFs | ANN6 | ||||||
|---|---|---|---|---|---|---|---|---|
\(h^{(6)}_{8,1}(r)\) | \({\mathbb {R}}_{8,1}^{(6)}(r)\) | GA | Error | AST | Error | GA-AST | Error | |
0.0 | 1.160819819659 | \(0.0000_{-0}\) | 1.16093104 | \(1.4441_{-4}\) | 1.16081999 | \(7.3822_{-8}\) | 1.16081956 | \(2.5447_{-7}\) |
0.1 | 1.160297689045 | \(5.3263_{-9}\) | 1.16040234 | \(6.4940_{-4}\) | 1.16029785 | \(7.6417_{-7}\) | 1.16029763 | \(2.3650_{-6}\) |
0.2 | 1.158730315169 | \(1.4361_{-9}\) | 1.15880759 | \(4.4537_{-4}\) | 1.15873046 | \(8.3864_{-7}\) | 1.15873036 | \(2.5593_{-6}\) |
0.3 | 1.156114745862 | \(1.7157_{-10}\) | 1.15616949 | \(2.2727_{-4}\) | 1.15611490 | \(7.4055_{-7}\) | 1.15611477 | \(2.6446_{-7}\) |
0.4 | 1.152446041165 | \(5.7457_{-11}\) | 1.15249490 | \(7.0943_{-4}\) | 1.15244622 | \(1.0099_{-6}\) | 1.15244604 | \(1.5218_{-6}\) |
0.5 | 1.147717243642 | \(7.6349_{-11}\) | 1.14777601 | \(6.8283_{-4}\) | 1.14771742 | \(1.3692_{-6}\) | 1.14771726 | \(4.0837_{-7}\) |
0.6 | 1.141919336231 | \(2.1342_{-11}\) | 1.14199556 | \(1.7497_{-4}\) | 1.14191949 | \(4.4069_{-7}\) | 1.14191936 | \(9.1817_{-7}\) |
0.7 | 1.135041187165 | \(1.9892_{-11}\) | 1.13513234 | \(5.3114_{-4}\) | 1.13504133 | \(2.0408_{-6}\) | 1.13504121 | \(4.1913_{-7}\) |
0.8 | 1.127069481243 | \(2.6313_{-11}\) | 1.12716571 | \(9.8891_{-4}\) | 1.12706964 | \(5.5233_{-7}\) | 1.12706950 | \(6.4930_{-7}\) |
0.9 | 1.117988636564 | \(2.0657_{-11}\) | 1.11807882 | \(6.5764_{-4}\) | 1.11798881 | \(2.9974_{-6}\) | 1.11798866 | \(1.1377_{-7}\) |
1.0 | 1.107780705617 | \(1.6943_{-11}\) | 1.10786089 | \(8.4893_{-6}\) | 1.10778087 | \(2.5239_{-9}\) | 1.10778073 | \(4.4627_{-10}\) |
