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Table 1 Comparison of absolute errors between the regularized solutions \(\pmb{v_{m}}\) of \(\pmb{m=10^{2}}\) and \(\pmb{m=10^{10}}\)

From: On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data

( 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