Research Article
A Nonclassical Radau Collocation Method for Nonlinear Initial-Value Problems with Applications to Lane-Emden Type Equations
Table 3
Comparison of numerical results for
(
) for Example
4.2.
| | | Present method | Method in [10] | Method in [15] | Method in [16] | Exact [21] |
| | 0 | 20 | 2.4494897427832 | 2.44899 | — | — | 2.4494897427832 | | 0.5 | 27 | 2.752698051 | — | — | — | 2.75269805 | | 1 | 20 | 3.1415926535898 | 3.14048 | — | — | 3.1415926535898 | | 1.5 | 25 | 3.65375374 | — | — | 3.65375374 | 3.65375374 | | 2 | 15 | 4.35287460 | 4.35086 | 4.352875 | 4.35287460 | 4.35287460 | | 2.5 | 17 | 5.35527546 | — | — | 5.35527546 | 5.35527546 | | 3 | 25 | 6.89684862 | 6.89312 | 6.896846 | 6.89684862 | 6.89684862 | | 3.5 | 25 | 9.53580535 | — | — | — | 9.53580534 | | 4 | 30 | 14.9715464 | 14.96518 | 14.971546 | 14.9715463 | 14.9715463 | | 4.5 | 30 | 31.8364633 | — | — | — | 31.8364632 |
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