Table 1 Comparison of absolute errors between the regularized solutions \(\pmb{v_{m}}\) of \(\pmb{m=10^{2}}\) and \(\pmb{m=10^{10}}\)
( x , t , s ) | Exact value | App. value 1 ( \(\boldsymbol {m=10^{2}}\) ) | App. value 2 ( \(\boldsymbol {m=10^{10}}\) ) | Abs. error 1 | Abs. error 2 |
|---|---|---|---|---|---|
\((\frac{\pi}{2},0.75,0.75 )\) | 0.1053992246 | 0.0915741799 | 0.1053992172 | 0.0138250446 | 7.4E−09 |
\((\frac{\pi}{2},0.5,0.5 )\) | 0.2231301601 | 0.1684339068 | 0.2231301293 | 0.0546962533 | 3.08E−08 |
\((\frac{\pi}{2},0.25,0.25 )\) | 0.4723665527 | 0.3098032761 | 0.4723664549 | 0.1625632766 | 9.87E−08 |
\((\frac{\pi}{2},0.125,0.125 )\) | 0.6872892788 | 0.4201595585 | 0.6872891127 | 0.2671297203 | 1.661E−07 |
\((\frac{\pi}{2},0,0 )\) | 1 | 0.5698263001 | 0.9999997239 | 0.4301736999 | 2.761E−07 |