A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

Table 2

Absolute error of Example 5.3′s exact and approximated solution.

𝑥	Approximated solution	Exact solution	Absolute error
0	0	0	0
0.1	−1.990065975846963e−002	−1.990066170633618e−002	1.947866552082234e−009
0.2	−7.844142227675365e−002	−7.844142630656266e−002	4.029809014260977e−009
0.3	−1.723553877014332e−001	−1.723553924821048e−001	4.780671636339662e−009
0.4	2.968400304512400e−001	−2.968400102365468e−001	2.021469319712921e−008
0.5	−4.462871382464894e−001	−4.462871026284195e−001	3.561806982688154e−008
0.6	−6.149693761315079e−001	−6.149693994959211e−001	2.336441318195881e−008
0.7	−7.975522016254086e−001	−7.975522399147356e−001	3.828932693128451e−008
0.8	−9.893925027250091e−001	−9.893924836722143e−001	1.905279478631172e−008
0.9	−1.186653691831187e+000	−1.186653690555469e+000	1.275718419790906e−009
1.0	−1.386294358347456e+000	−1.386294361119891e+000	2.772434948283831e−009