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## An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order

#### Mehdi DELKHOSH [1] , Kourosh PARAND [2]

The Lane-Emden type equations of arbitrary (fractional and integer) order and the white dwarf equation are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. In this paper, an efficient numerical algorithm based on the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) and the collocation method to solve these well-known differential equations is presented. The operational matrices of the fractional derivative and the product of order $\alpha$ in the Caputo's definition for the GFCFs are used. The obtained results are compared with other results to verify the accuracy and efficiency of the presented method. The obtained numerical results are better than other proposed methods.
fractional order of the Chebyshev functions, Lane-Emden type equations, operational matrix, Tau-Collocation method, white dwarf equation
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-6632-4743Author: Mehdi DELKHOSH Institution: Shahid Beheshti UniversityCountry: Iran Orcid: 0000-0001-5946-0771Author: Kourosh PARAND (Primary Author)Institution: Shahid Beheshti UniversityCountry: Iran Publication Date : December 8, 2019
 Bibtex @research article { hujms656646, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1601 - 1619}, doi = {}, title = {An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order}, key = {cite}, author = {DELKHOSH, Mehdi and PARAND, Kourosh} } APA DELKHOSH, M , PARAND, K . (2019). An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1601-1619 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/50516/656646 MLA DELKHOSH, M , PARAND, K . "An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1601-1619 Chicago DELKHOSH, M , PARAND, K . "An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1601-1619 RIS TY - JOUR T1 - An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order AU - Mehdi DELKHOSH , Kourosh PARAND Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1601 EP - 1619 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order %A Mehdi DELKHOSH , Kourosh PARAND %T An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R %U ISNAD DELKHOSH, Mehdi , PARAND, Kourosh . "An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1601-1619 . AMA DELKHOSH M , PARAND K . An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1601-1619. Vancouver DELKHOSH M , PARAND K . An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1619-1601.