Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima”

Table 1

Values of the successive lower/upper approximations 𝛼_𝑘(𝑡) and 𝛽_𝑘(𝑡+.85).

𝑡	1.50	1.55	1.60	1.65	1.70	1.75
𝛽1(𝑡+.85)	0.2500000	0.2396285	0.2326388	0.2286608	0.2273177	0.2281468
𝛽2(𝑡+.85)	0.0625000	0.0795487	0.0954878	0.1138875	0.1307175	0.1464314
𝛽3(𝑡+.85)	0.0156250	0.0322634	0.0490684	0.0671041	0.0850914	0.1029515
𝛽4(𝑡+.85)	0.0039063	0.0211106	0.0383552	0.0558882	0.0734248	0.0909491
𝛽5(𝑡+.85)	0.0009766	0.0183982	0.0358232	0.0532996	0.0707523	0.0881732
𝛼5(𝑡)	−0.0009766	−0.0236676	−0.0416446	−0.0552493	−0.0648509	−0.0708277
𝛼4(𝑡)	−0.0039063	−0.0269991	−0.0452915	−0.0591247	−0.0688717	−0.0749110
𝛼3(𝑡)	−0.0156250	−0.0399773	−0.0590208	−0.0731539	−0.0828101	−0.0884511
𝛼2(𝑡)	−0.0625000	−0.0871172	−0.1048556	−0.1164338	−0.1225992	−0.1243204
𝛼1(𝑡)	−0.2500000	−0.2427252	−0.2336358	−0.2230384	−0.2111877	−0.1982954