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

Table 5

Vanishing of the Bernoulli coefficients as the number of index is increased.

𝑁=8	Example 2	Example 3	Example 4	Example 5	Example 6
𝑐0	+0.946083	+0.948962	+0.951426	+0.954020	−0.053961
𝑐1	−0.158529	−0.144942	−0.133975	−0.136343	−0.158828
𝑐2	−0.150584	−0.126065	−0.108253	−0.132283	−0.151451
𝑐3	+0.015700	+0.035408	+0.046539	+0.008232	+0.014332
𝑐4	+0.007379	+0.012099	+0.011798	+0.004384	+0.006137
𝑐5	−0.000558	−0.005891	+0.011145	+0.000293	−0.001159
𝑐6	−0.000174	−0.000918	−0.001069	+0.000050	−0.000277
𝑐7	+0.000011	+0.001152	+0.003566	+0.000041	+0.000106
𝑐8	+0.000002	−0.000076	−0.001424	−0.000010	+0.000010