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

Table 4

The exact and approximated solution of Example 6 together with the error comparisons.

𝑥	Solution of PM	Exact Solution [35]	Error at 𝑁=10	Error of [1]	Error [36] 𝑁=25
0.0	1.0000000000	1.0000000000	0.0𝑒+0.0	0.0𝑒+0.0	0.0𝑒+0.0
0.1	0.9983366595	0.9983367000	4.05𝑒−08	2.50𝑒−04	4.04𝑒−08
0.2	0.9933862135	0.9933862000	1.35𝑒−08	2.48𝑒−04	1.35𝑒−08
0.5	0.9603109023	0.9603109000	2.33𝑒−09	2.05𝑒−04	2.34𝑒−09
1.0	0.8608138122	0.8608138000	1.22𝑒−08	1.93𝑒−04	1.22𝑒−08