Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 8 Comparing numerical results of the RCC method with Runge–Kutta of fourth order at \(m=5\)

x	Exact values	Runge–Kutta	RCC method
x	Exact values	Runge–Kutta	N = 20	N = 25
0.0	1	1	1	1
0.2	0.9933992678	0.9933992543126849	0.9933992939	0.9933992684
0.4	0.9743547036	0.9743546989480394	0.9743547291	0.9743547043
0.6	0.9449111825	0.9449111812575188	0.9449112047	0.9449111830
0.8	0.9078412990	0.9078412996319103	0.9078413170	0.9078412994
1.0	0.8660254037	0.8660254054870272	0.8660254037	0.8660254041
1.2	0.8219949365	0.8219949387903671	0.8219949365	0.8219949367
1.4	0.7777137711	0.7777137735378965	0.7777137710	0.7777137716
1.6	0.7345531603	0.7345531628136189	0.7345531609	0.7345531712
1.8	0.6933752452	0.6933752476639488	0.6933752245	0.6933753566
2.0	0.6546536707	0.6546536728956738	0.6546535327	0.6546543517