Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

Mostafa M A Khater,S K Elagan,M A El-Shorbagy,S H Alfalqi,J F Alzaidi,Nawal A Alshehri

Table 1. Absolute errors between the analysis obtained using the ESE method and the constructed semi-analytical solution using the VI scheme for different values of x and the following values of the abovementioned parameters: a0 = 1, h2 = 0, h1 = −1, h3 = 1, r1 = −1, and r2 = −2.

Value of x t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 t = 8 t = 9 t = 10 0 0.071 941 14 3.999 959 59 3.999 963 58 3.999 934 56 3.999 897 1 3.999 851 19 3.999 796 84 3.999 734 05 3.999 662 819 3.999 583 142 1 0.009 889 99 3.999 816 27 3.999 995 07 3.999 991 14 3.999 986 07 3.999 979 86 3.999 972 51 3.999 964 01 3.999 954 368 3.999 943 585 2 0.001 341 33 3.998 658 31 3.999 999 33 3.999 998 8 3.999 998 12 3.999 997 27 3.999 996 28 3.999 995 13 3.999 993 824 3.999 992 365 3 0.000 181 58 3.990 109 47 3.999 999 91 3.999 999 84 3.999 999 74 3.999 999 63 3.999 999 5 3.999 999 34 3.999 999 164 3.999 998 967 4 2.4575E-05 3.928 055 15 3.999 999 98 3.999 999 98 3.999 999 97 3.999 999 95 3.999 999 93 3.999 999 91 3.999 999 887 3.999 999 86 5 3.3259E-06 3.523 188 31 3.999 999 94 4 4 3.999 999 99 3.999 999 99 3.999 999 99 3.999 999 985 3.999 999 981 6 4.5012E-07 2 3.999 999 55 4 4 4 4 4 3.999 999 998 3.999 999 997 7 6.0917E-08 0.476 811 69 3.999 996 67 4 4 4 4 4 4 4 8 8.2442E-09 0.071 944 84 3.999 975 42 4 4 4 4 4 4 4 9 1.1157E-09 0.009 890 49 3.999 818 41 4 4 4 4 4 4 4 10 1.51E-10 0.001 341 4 3.998 658 6 4 4 4 4 4 4 4 11 2.0435E-11 0.000 181 59 3.990 109 51 4 4 4 4 4 4 4 12 2.7656E-12 2.4577E-05 3.928 055 16 3.999 999 99 4 4 4 4 4 4 13 3.7437E-13 3.3261E-06 3.523 188 31 3.999 999 94 4 4 4 4 4 4 14 5.0626E-14 4.5014E-07 2 3.999 999 55 4 4 4 4 4 4 15 6.8834E-15 6.092E-08 0.476 811 69 3.999 996 67 4 4 4 4 4 4 16 8.8818E-16 8.2446E-09 0.071 944 84 3.999 975 42 4 4 4 4 4 4 17 2.2204E-16 1.1158E-09 0.009 890 49 3.999 818 41 4 4 4 4 4 4 18 0 1.5101E-10 0.001 341 4 3.998 658 6 4 4 4 4 4 4 19 0 2.0436E-11 0.000 181 59 3.990 109 51 4 4 4 4 4 4 20 0 2.7658E-12 2.4577E-05 3.928 055 16 3.999 999 99 4 4 4 4 4 21 0 3.7437E-13 3.3261E-06 3.523 188 31 3.999 999 94 4 4 4 4 4 22 0 5.0626E-14 4.5014E-07 2 3.999 999 55 4 4 4 4 4 23 0 6.8834E-15 6.092E-08 0.476 811 69 3.999 996 67 4 4 4 4 4 24 0 8.8818E-16 8.2446E-09 0.071 944 84 3.999 975 42 4 4 4 4 4 25 0 2.2204E-16 1.1158E-09 0.009 890 49 3.999 818 41 4 4 4 4 4 26 0 0 1.5101E-10 0.001 341 4 3.998 658 6 4 4 4 4 4 27 0 0 2.0436E-11 0.000 181 59 3.990 109 51 4 4 4 4 4 28 0 0 2.7658E-12 2.4577E-05 3.928 055 16 3.999 999 99 4 4 4 4 29 0 0 3.7437E-13 3.3261E-06 3.523 188 31 3.999 999 94 4 4 4 4 30 0 0 5.0626E-14 4.5014E-07 2 3.999 999 55 4 4 4 4