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Table 8 The solutions obtained by the new modified Ishikawa iteration method for different values of λ and γ

From: The new modified Ishikawa iteration method for the approximate solution of different types of differential equations

x

λ = 0.5, γ = 0.5

λ = 0.5, γ = 0.25

λ = 0.25, γ = 0.5

λ = 0.25, γ = 0.25

x = 0.6

y 1 = 0.072 y 2 = 0.036 y 3 = 0.054 y 4 = 0.044999928 y 5 = 0.049499985 y 6 = 0.047249996 y 7 = 0.048376997 y 8 = 0.047812496 y 9 = 0.048093746 y 10 = 0.047953121 y 11 = 0.048023434

y 1 = 0.072 y 2 = 0.017999992 y 3 = 0.044999996 y 4 = 0.024749993 y 5 = 0.034874994 y 6 = 0.027281243 y 7 = 0.031078119 y 8 = 0.028230462 y 9 = 0.02965429 y 10 = 0.028586419 y 11 = 0.029120355

y 1 = 0.072 y 2 = 0.036 y 3 = 0.044999999 y 4 = 0.040499999 y 5 = 0.041624999 y 6 = 0.04062499 y 7 = 0.041203124 y 8 = 0.041132812 y 9 = 0.041115234 y 10 = 0.041124023 y 11 = 0.041121825

y 1 = 0.072 y 2 = 0.017999999 y 3 = 0.031499999 y 4 = 0.021374999 y 5 = 0.023906249 y 6 = 0.022007812 y 7 = 0.022482421 y 8 = 0.022126464 y 9 = 0.022215453 y 10 = 0.022148711 y 11 = 0.022165397

x = 1

y 1 = 0.333333 y 2 = 0.1666666 y 3 = 0.25 y 4 = 0.208333 y 5 = 0.2291666 y 6 = 0.218749983 y 7 = 0.223958321 y 8 = 0.221354152 y 9 = 0.222656236 y 10 = 0.222005194 y 11 = 0.222330715

y 1 = 0.333333 y 2 = 0.08333333 y 3 = 0.208333316 y 4 = 0.114583304 y 5 = 0.16145831 y 6 = 0.126302055 y 7 = 0.143880182 y 8 = 0.130696586 y 9 = 0.137288384 y 10 = 0.132344535 y 11 = 0.134816459

y 1 = 0.333333 y 2 = 0.1666666 y 3 = 0.20833333 y 4 = 0.187499999 y 5 = 0.192708333 y 6 = 0.190104166 y 7 = 0.190755207 y 8 = 0.190429686 y 9 = 0.190348306 y 10 = 0.190388996 y 11 = 0.190378823

y 1 = 0.333333 y 2 = 0.083333333 y 3 = 0.1458333333 y 4 = 0.098958333 y 5 = 0.110677083 y 6 = 0.10188802 y 7 = 0.104085285 y 8 = 0.102437336 y 9 = 0.102849323 y 10 = 0.102540332 y 11 = 0.10261758

x = 1.5

y 1 = 1.125 y 2 = 0.5625 y 3 = 0.84375 y 4 = 0.703123875 y 5 = 0.773437275 y 6 = 0.738281192 y 7 = 0.755859333 y 8 = 0.747070263 y 9 = 0.751464796 y 10 = 0.749267529 y 11 = 0.750366163

y 1 = 1.125 y 2 = 0.2812499888 y 3 = 0.703124941 y 4 = 0.38654901 y 5 = 0.544921796 y 6 = 0.426269435 y 7 = 0.485595614 y 8 = 0.441100977 y 9 = 0.463348296 y 10 = 0.446662805 y 11 = 0.455005549

y 1 = 1.125 y 2 = 0.5625 y 3 = 0.703124998 y 4 = 0.632812496 y 5 = 0.650390623 y 6 = 0.64160156 y 7 = 0.643798823 y 8 = 0.64270019 y 9 = 0.642425532 y 10 = 0.64256274 y 11 = 0.642528527

y 1 = 1.125 y 2 = 0.281249998 y 3 = 0.492187499 y 4 = 0.333984373 y 5 = 0.373535155 y 6 = 0.343872067 y 7 = 0.351287836 y 8 = 0.345726009 y 9 = 0.347116465 y 10 = 0.34607362 y 11 = 0.346334332