Table 1 Adomian decomposition approachs outcome.
Value of \(\xi\) | Exact sol. | Approx. sol. | Absolute error | Value of \(\xi\) | Exact sol. | Approx. sol. | Absolute error |
|---|---|---|---|---|---|---|---|
\(-0.030\) | 0.775258744695 | 0.771788871147 | 3.4698735480E-03 | 0.001 | 1.00852138341 | 1.00851636004 | 5.0233700000E-06 |
\(-0.029\) | 0.781865021704 | 0.778569547058 | 3.2954746460E-03 | 0.002 | 1.0171153808 | 1.01709519531 | 2.0185490000E-05 |
\(-0.028\) | 0.788527593331 | 0.785408113907 | 3.1194794240E-03 | 0.003 | 1.02578261094 | 1.02573698955 | 4.5621390000E-05 |
\(-0.027\) | 0.795246939287 | 0.792304127249 | 2.9428120380E-03 | 0.004 | 1.03452369787 | 1.03444223526 | 8.1462610000E-05 |
\(-0.026\) | 0.802023543365 | 0.799257212696 | 2.7663306690E-03 | 0.005 | 1.04333927095 | 1.04321143287 | 1.2783808000E-04 |
\(-0.025\) | 0.808857893485 | 0.806267061358 | 2.5908321270E-03 | 0.006 | 1.05222996491 | 1.05204509038 | 1.8487453000E-04 |
\(-0.024\) | 0.815750481723 | 0.813333425592 | 2.4170561310E-03 | 0.007 | 1.06119641988 | 1.06094372255 | 2.5269733000E-04 |
\(-0.023\) | 0.822701804348 | 0.82045611498 | 2.2456893680E-03 | 0.008 | 1.07023928145 | 1.06990785055 | 3.3143090000E-04 |
\(-0.022\) | 0.829712361858 | 0.82763499262 | 2.0773692380E-03 | 0.009 | 1.07935920071 | 1.07893800143 | 4.2119928000E-04 |
\(-0.021\) | 0.836782659016 | 0.834869971626 | 1.9126873900E-03 | 0.010 | 1.0885568343 | 1.08803470752 | 5.2212678000E-04 |
\(-0.020\) | 0.843913204889 | 0.842161011894 | 1.7521929950E-03 | 0.011 | 1.09783284445 | 1.09719850619 | 6.3433826000E-04 |
\(-0.019\) | 0.851104512875 | 0.849508117011 | 1.5963958640E-03 | 0.012 | 1.10718789905 | 1.10642993924 | 7.5795981000E-04 |
\(-0.018\) | 0.858357100755 | 0.856911331456 | 1.4457692990E-03 | 0.013 | 1.11662267164 | 1.11572955269 | 8.9311895000E-04 |
\(-0.017\) | 0.865671490716 | 0.864370737897 | 1.3007528190E-03 | 0.014 | 1.12613784156 | 1.12509789635 | 1.0399452100E-03 |
\(-0.016\) | 0.873048209399 | 0.871886454723 | 1.1617546760E-03 | 0.015 | 1.13573409388 | 1.13453552342 | 1.1985704600E-03 |
\(-0.015\) | 0.880487787931 | 0.879458633682 | 1.0291542490E-03 | 0.016 | 1.14541211955 | 1.14404299025 | 1.3691293000E-03 |
\(-0.014\) | 0.887990761963 | 0.887087457708 | 9.0330425500E-04 | 0.017 | 1.15517261539 | 1.15362085603 | 1.5517593600E-03 |
\(-0.013\) | 0.895557671713 | 0.894773138863 | 7.8453285000E-04 | 0.018 | 1.16501628416 | 1.16326968255 | 1.7466016100E-03 |
\(-0.012\) | 0.903189062003 | 0.902515916446 | 6.7314555700E-04 | 0.019 | 1.1749438346 | 1.1729900338 | 1.9538008000E-03 |
\(-0.011\) | 0.910885482296 | 0.91031605518 | 5.6942711600E-04 | 0.020 | 1.1849559815 | 1.18278247589 | 2.1735056100E-03 |
\(-0.010\) | 0.918647486737 | 0.91817384349 | 4.7364324700E-04 | 0.021 | 1.19505344575 | 1.19264757678 | 2.4058689700E-03 |
\(-0.009\) | 0.926475634194 | 0.926089591991 | 3.8604220300E-04 | 0.022 | 1.20523695436 | 1.20258590596 | 2.6510484000E-03 |
\(-0.008\) | 0.934370488296 | 0.934063631967 | 3.0685632900E-04 | 0.023 | 1.21550724055 | 1.21259803445 | 2.9092061000E-03 |
\(-0.007\) | 0.942332617478 | 0.942096313995 | 2.3630348300E-04 | 0.024 | 1.22586504379 | 1.22268453438 | 3.1805094100E-03 |
\(-0.006\) | 0.950362595015 | 0.950188006637 | 1.7458837800E-04 | 0.025 | 1.23631110984 | 1.23284597906 | 3.4651307800E-03 |
\(-0.005\) | 0.958460999069 | 0.958339095237 | 1.2190383200E-04 | 0.026 | 1.24684619083 | 1.24308294257 | 3.7632482600E-03 |
\(-0.004\) | 0.96662841273 | 0.966549980753 | 7.8431977000E-05 | 0.027 | 1.25747104528 | 1.25339599991 | 4.0750453700E-03 |
\(-0.003\) | 0.974865424053 | 0.974821078703 | 4.4345350000E-05 | 0.028 | 1.26818643819 | 1.26378572658 | 4.4007116100E-03 |
\(-0.002\) | 0.983172626109 | 0.983152818168 | 1.9807941000E-05 | 0.029 | 1.27899314107 | 1.27425269853 | 4.7404425400E-03 |
\(-0.001\) | 0.991550617018 | 0.991545640801 | 4.9762169999E-06 | 0.030 | 1.28989193201 | 1.2847974922 | 5.0944398100E-03 |