1 Introduction
2 Preliminaries
3 Some Δ-convergence and strong convergence theorems
4 Numerical example
Step | When \(u_{1} = 0.25\) |
\(u_{1} = 0.45\)
|
\(u_{1} = 0.65\)
|
---|---|---|---|
1 | 0.25 | 0.45 | 0.65 |
2 | 0.1607142857142857 | 0.2892857142857142 | 0.4178571428571429 |
3 | 0.1071428571428571 | 0.1928571428571428 | 0.2785714285714286 |
4 | 0.07247899159663865 | 0.1304621848739496 | 0.1884453781512605 |
5 | 0.04941749427043545 | 0.0889514896867838 | 0.1284854851031322 |
6 | 0.03386013496307614 | 0.06094824293353705 | 0.088036350903998 |
7 | 0.02327884278711485 | 0.04190191701680672 | 0.0605249912464986 |
8 | 0.01604352678571429 | 0.02887834821428571 | 0.04171316964285715 |
9 | 0.01107767325680272 | 0.0199398118622449 | 0.02880195046768708 |
10 | 0.007660093209491246 | 0.01378816777708424 | 0.01991624234467724 |
11 | 0.005303141452724708 | 0.00954565461490447 | 0.01378816777708424 |
12 | 0.003674983989168876 | 0.006614971180503976 | 0.00955495837183908 |
13 | 0.002548779218294543 | 0.004587802592930178 | 0.006626825967565813 |
14 | 0.001768928860458153 | 0.003184071948824675 | 0.004599215037191199 |
15 | 0.001228422819762606 | 0.002211161075572691 | 0.003193899331382777 |
16 | 0.000853514556588304 | 0.001536326201858948 | 0.002219137847129592 |
17 | 0.0005932967039699188 | 0.001067934067145854 | 0.00154257143032179 |
18 | 0.0004125798918411505 | 0.0007426438053140709 | 0.001072707718786992 |
19 | 0.0002870120986721047 | 0.0005166217776097884 | 0.0007462314565474726 |
20 | 0.0001997249140244027 | 0.0003595048452439249 | 0.0005192847764634474 |
21 | 0.0001390242048601234 | 0.0002502435687482223 | 0.0003614629326363212 |
22 | 0.0000967972267484037 | 0.0001742350081471267 | 0.0002516727895458498 |
23 | 0.00006741235434263828 | 0.0001213422378167489 | 0.0001752721212908597 |
24 | 0.0000469581784523506 | 0.0000845247212142311 | 0.0001220912639761116 |
25 | 0.00003271676367581804 | 0.0000588901746164725 | 0.000085063585557127 |
26 | 0.00002279868964810942 | 0.00004103764136659699 | 0.00005927659308508453 |
27 | 0.000015889995815349 | 0.00002860199246762819 | 0.00004131398911990741 |
28 | 0.00001107660292237831 | 0.00001993788526028096 | 0.00002879916759818363 |
29 | 7.722420347291922 × 10−6 | 0.00001390035662512546 | 0.00002007829290295901 |
30 | 5.384680854404231 × 10−6 | 9.69242553792 × 10−6 | 0.00001400017022145 |
31 | 3.755106385308214 × 10−6 | 6.759191493554787 × 10−6 | 9.76327660180 × 10−6 |
Step | When \(u_{1} = 1.5\) |
\(u_{1} = 2.5\)
|
\(u_{1} = 3.5\)
|
---|---|---|---|
1 | 1.5 | 2.5 | 3.5 |
50 | 1.000070736246516 | 2.000070736246516 | 3.000070736246516 |
100 | 1.000000020810691 | 2.000000020810692 | 3.000000020810691 |
150 | 1.000000000006688 | 2.000000000006688 | 3.000000000006689 |
200 | 0.1721565830342946 | 1.090775274459172 | 2.056164187502003 |
250 | 0.00005853496173392133 | 1.00003086450209 | 2.000019096386024 |
300 | 2.015550211966978 × 10−8 | 1.000000010627658 | 2.000000006575511 |
350 | 7.001008916808291 × 10−12 | 1.000000000003692 | 2.000000000002284 |
400 | 2.447383506364153 × 10−15 | 0.0918987936870247 | 1.030161439675001 |
450 | 8.59732107577053 × 10−19 | 0.00003228278010981194 | 1.000010595298216 |
500 | 3.031773634861876 × 10−22 | 1.13842533894431 × 10−8 | 1.000000003736344 |
550 | 1.072466692421632 × 10−25 | 4.027092404879379 × 10−12 | 1.000000000001322 |
600 | 3.803545320138658 × 10−29 | 1.42822416570892 × 10−15 | 0.03556653915576083 |
650 | 1.351861194143804 × 10−32 | 5.076213541974867 × 10−19 | 0.00001264110719020337 |