Table 2: Comparison numerical solution (RKF45) for (7.1) and its first order approximate solutions given by RBHPM (7.8), LPRBHPM (7.11), HPM (7.15), and HPM (7.16).

Order 2 4
RKF45 for (7.1) RBHPM (7.8) LPRBHPM (7.11) HPM (7.15) HPM (7.16)

0.00 0.000000000000 0.000000000000 −2.04249011 (−13) 0.000000000000 0.000000000000
0.10 0.094996749389 0.0963305722762 0.0963305680033 0.095001281746 0.0949968616125
0.20 0.179964338949 0.181413957989 0.181413692649 0.180042107937 0.179964612584
0.30 0.254886117960 0.255755918036 0.255752978888 0.255328628571 0.254889069792
0.40 0.319824133934 0.319864038194 0.319847953401 0.321424660317 0.319850515572
0.50 0.374962243912 0.374261968751 0.374202151797 0.379476686508 0.3751195795
0.60 0.420620714410 0.419505461842 0.419331298484 0.431478857143 0.421336349604
0.70 0.457249830610 0.456198011306 0.455769940137 0.480583988889 0.459927483684
0.80 0.485408608033 0.485004250862 0.484075378004 0.531466565079 0.49405125938
0.90 0.505735525317 0.506659764874 0.504828319804 0.590743735714 0.53057647436
1.00 0.518917385708 0.521976574206 0.518630236646 0.66746031746 0.583931084348
1.10 0.525660073662 0.531844221386 0.526097880422 0.773643793651 0.683143422756
1.20 0.526664476070 0.537227026265 0.527855737463 0.924935314286 0.884097382101
1.30 0.522608206722 0.539158647966 0.524527343795 1.14130269603 1.2900013214
1.40 0.514133103782 0.538735520529 0.516726377800 1.44784142222 2.08441286596
1.50 0.501837942107 0.537111006964 0.505048313285 1.87566964286 3.58297069111
1.60 0.486275223293 0.535492254682 0.490063208382 2.4629231746 6.31238329453
1.70 0.467950980699 0.535141785803 0.472309972142 3.25585650079 11.128360908
1.80 0.447326548414 0.537385900716 0.452292231487 4.31005577143 19.3882241197
1.90 0.424821677896 0.54363212026 0.430475743238 5.69176980317 33.1990855168
2.00 0.400817960941 0.555398274173 0.407287171967 7.47936507937 55.769016169
2.10 0.375662771298 0.574356631824 0.383113985298 9.76491075 91.8967515218
2.20 0.349672525187 0.602397906631 0.358305196653 12.6558996317 148.645576503
2.30 0.323136129463 0.641722425466 0.333172699524 16.2771112079 236.259417439
2.40 0.296317411714 0.694969880802 0.307992974314 20.7726226286 369.394267712
2.50 0.269457558120 0.765406030734 0.28300899685 26.3079737103 568.756347393
2.60 0.242776634418 0.857196643743 0.258432227399 33.0724919365 863.260364544
2.70 0.216475028642 0.975820118585 0.234444603854 41.2817834571 1292.84749061
2.80 0.190734203918 1.12870912808 0.211200498849 51.1803960889 1912.13383476
2.90 0.165717437177 1.32628670185 0.188828626412 63.0446603151 2795.09702573
3.00 0.141570064350 1.58371504978 0.167433899647 77.1857142857 4041.05178634

A.A.E. 0.231 0.00641 12.1 401