A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation

Table 1

The exact and approximated solution of Example 3 together with the error comparisons for 𝑁=10.

𝑥	Solution of PM	Exact Solution [7]	Error of PM	Error of [4]	Error of [1]
0.0	+3.01060𝑒−31	+0.0000000000	3.01𝑒−31	9.24𝑒−18	0.00𝑒+00
0.1	−0.0016658339	−0.0016658338	6.21𝑒−11	5.28𝑒−10	5.85𝑒−07
0.2	−0.0066533671	−0.0066533671	9.22𝑒−13	3.37𝑒−08	6.04𝑒−07
0.5	−0.0411539573	−0.0411539567	5.95𝑒−10	8.12𝑒−06	5.58𝑒−07
1.0	−0.1588276831	−0.1588272857	3.97𝑒−07	4.93𝑒−04	8.20𝑒−07