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