Quasilinearization of the Initial Value Problem for Difference Equations with “Maxima”

Table 1

Values of successive approximations 𝛼_𝑛(𝑘) and 𝛽_𝑛(𝑘), 𝑛=1,2,3,4,5.

𝑘	1	2	3
𝛽1(𝑘)	0.126984126984127	0.126984126984127	0.126984126984127
𝛽2(𝑘)	0.00245312888643079	0.00245312888643079	0.0025469207078195
𝛽3(𝑘)	5.93137225955726E-07	5.93137225955726E-07	9.79796674723704E-07
𝛽4(𝑘)	2.96900520626677E-14	2.96900520626677E-14	9.99338575141566E-14
𝛽5(𝑘)	2.13083324289133E-17	2.13083324289133E-17	1.43434637320051E-16
𝛼5(𝑘)	−1.16621056078124E-17	−1.16621056078124E-17	−6.48937233257787E-18
𝛼4(𝑘)	−4.08173696273438E-17	−4.08173696273438E-17	−2.74428886272319E-15
𝛼3(𝑘)	−7.22563191957548E-09	−7.22563191957548E-09	−2.43398432836776E-07
𝛼2(𝑘)	−0.000449855202856569	−0.000449855202856569	−0.00207365792650451
𝛼1(𝑘)	−0.115942028985507	−0.115942028985507	−0.126023944549464