2013
DOI: 10.1007/s10569-013-9477-8
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Solving non-linear Lane–Emden type equations using Bessel orthogonal functions collocation method

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Cited by 33 publications
(32 citation statements)
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“…Pandey and Kumar 22 proposed a numerical technique based on Bernstein operational matrix of differentiation for the solution of singular initial value problems of Lane-Emden type. Several methods based on splines, 23,24 collocation techniques, [25][26][27][28][29] and pseudospectral technique 30,31 have been proposed to solve (3). Some nonperturbation methods such as HPM, [32][33][34][35] VIM, 36,37 ADM, 38 homotopy analysis method (HAM), [39][40][41] and OHAM [42][43][44] have been applied to solve Lane-Emden-type problem.…”
Section: Introductionmentioning
confidence: 99%
“…Pandey and Kumar 22 proposed a numerical technique based on Bernstein operational matrix of differentiation for the solution of singular initial value problems of Lane-Emden type. Several methods based on splines, 23,24 collocation techniques, [25][26][27][28][29] and pseudospectral technique 30,31 have been proposed to solve (3). Some nonperturbation methods such as HPM, [32][33][34][35] VIM, 36,37 ADM, 38 homotopy analysis method (HAM), [39][40][41] and OHAM [42][43][44] have been applied to solve Lane-Emden-type problem.…”
Section: Introductionmentioning
confidence: 99%
“…The test functions are used to ensure that the differential equation and perhaps some boundary conditions are satisfied as closely as possible by the truncated series expansion. This is achieved by minimizing the residual function that is produced by using the truncated expansion instead of the exact solution with respect to a suitable norm [1,2,3,4,5,6,7,8,9, 10].…”
Section: Spectral Methodsmentioning
confidence: 99%
“…The Lane-Emden differential equations are very important in astrophysics, for this reason, writing articles to review them [61,62,63,64,65]. Now, we consider the linear Lane-Emden equation of fractional order as follows with the initial conditions…”
Section: Illustrative Examplesmentioning
confidence: 99%