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Table 5 The comparison with exact solution

From: Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane–Emden type differential equations (LETDEs)

\(\tau\)

LT-HPM

Exact

Error

0.0

1

1

0.0

0.1

1.010050167

1.010050167

0.0

0.2

1.040810773

1.040810774

1E−9

0.3

1.094174234

1.094174284

5E–8

0.4

1.173509973

1.173510871

8.98E−7

0.5

1.284016927

1.284025417

8.49E−6

0.6

1.43327584

1.433329415

0.19904038

0.7

1.632060167

1.63231622

2.56053E−4

0.8

1.895481173

1.896480879

9.99706E−4

0.9

2.359156039

2.247907987

−0.111248052

1.0

2.708333333

2.718281828

0.009948495

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