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Table 9 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 = 0.75, γ = 0.25

λ = 0.25, γ = 0.75

λ = 0.75, γ = 0.75

x = 0.6

y 1 = 0.072 y 2 = 0.017999999 y 3 = 0.058499999 y 4 = 0.028124999 y 5 = 0.050906249 y 6 = 0.033820312 y 7 = 0.046634765 y 8 = 0.037023925 y 9 = 0.044232055 y 10 = 0.038825957 y 11 = 0.042880531

y 1 = 0.072 y 2 = 0.054 y 3 = 0.058499999 y 4 = 0.057375 y 5 = 0.057656249 y 6 = 0.057585937 y 7 = 0.057603515 y 8 = 0.05759912 y 9 = 0.057600219 y 10 = 0.057599944 y 11 = 0.057600013

y 1 = 0.072 y 2 = 0.054 y 3 = 0.0675 y 4 = 0.064125 y 5 = 0.06665625 y 6 = 0.066023437 y 7 = 0.066498046 y 8 = 0.066379394 y 9 = 0.066468383 y 10 = 0.066446136 y 11 = 0.066462821

x = 1

y 1 = 0.333333 y 2 = 0.083333333 y 3 = 0.2708333 y 4 = 0.130208333 y 5 = 0.235677083 y 6 = 0.15657552 y 7 = 0.215901692 y 8 = 0.171407063 y 9 = 0.204778034 y 10 = 0.179749805 y 11 = 0.198520977

y 1 = 0.333333 y 2 = 0.25 y 3 = 0.270833333 y 4 = 0.265625 y 5 = 0.266927083 y 6 = 0.266601562 y 7 = 0.266682942 y 8 = 0.266662597 y 9 = 0.266667683 y 10 = 0.266666411 y 11 = 0.266666729

y 1 = 0.333333 y 2 = 0.25 y 3 = 0.3125 y 4 = 0.296875 y 5 = 0.30859375 y 6 = 0.305664062 y 7 = 0.307861328 y 8 = 0.307312011 y 9 = 0.307723998 y 10 = 0.307621001 y 11 = 0.307698249

x = 1.5

y 1 = 1.175 y 2 = 0.281249998 y 3 = 0.914062498 y 4 = 0.439453123 y 5 = 0.795410155 y 6 = 0.52844238 y 7 = 0.72866821 y 8 = 0.578498837 y 9 = 0.691125864 y 10 = 0.606655591 y 11 = 0.670008297

y 1 = 1.125 y 2 = 0.84375 y 3 = 0.914062498 y 4 = 0.896484375 y 5 = 0.900878905 y 6 = 0.899780271 y 7 = 0.900054929 y 8 = 0.899986264 y 9 = 0.90000343 y 10 = 0.899999137 y 11 = 0.90000021

y 1 = 1.125 y 2 = 0.84375 y 3 = 1.0546875 y 4 = 1.001953125 y 5 = 1.041503906 y 6 = 1.031616209 y 7 = 1.039031982 y 8 = 1.037178037 y 9 = 1.038568493 y 10 = 1.038220878 y 11 = 1.03848159