EULER POLYNOMIALS COLLOCATION METHOD FOR SOLVING LANE-EMDEN EQUATIONS
Abstract
In this paper, Euler polynomials were utilized to formulate a collocation method for approximating Lane-Emden equations. The approximation formulations were initialized producing truncation function. The residual functions were constructed by using the truncation function. The collocation points were substituted into the residual function to form system of equations and were solved by Matlab application fsolve or Newton-Raphson methods. The results were tabulated and compared with the Herodt (2004) results for absolute error. It was observed that the Euler polynomial is very accurate and converges faster producing zero error as compared. The study recommended in solving Lane-Emden and higher order equations.
References
BenRomdhance M and Temimi H 2018 An iterative numerical method for solving the LaneEmden initial and boundary value problems International Journal of Computational Methods 154 116 DOI: https://doi.org/10.1142/S0219876218500202
Catma G 2013 Bernoulli and Euler Polynomials MSc thesis Institute of Graduate Studies and Research Eastern Mediterranean University Gazimagusa North Cyprus86pp
Gholamreza H and Parand K 2011 An efficient computational algorithm for solving the nonlinear LaneEmden types equations International Journal of Mathematical and Computational Sciences 5813961401
Gospava B O and Gradimir V M 2014 Special classes of polynomial New edition University of Nis Faculty of Technology Leskovac Pp 1516
Horedt G P 2004Polytropes Applications in Astrophysics and Related Field Astrophysics and Space Science Library a series of books on the recent development of space science and of general geophysics and astrophysicsSpringerPp4678
Morteza B N 2020 A computational method for solving the LaneEmden initial value problems Journal of Computational Methods for Differential Equation 84 673684
Pandey R K Kumar N Bhardwaj A and Dutta G 2016 Solution of Lane Emden type equations using legendre operational matrix of differentiation Applied mathematics and computation 2181476297637
Parand K and Hashemi S 2018 Radial basis function differential quadrature method for solvingnonlinear differential equations of LaneEmden type Ain Shams Engineering Journal 94 615629
Parand K and Taghavi A 2008 Generalized Laguerre polynomials collocation method for solving LaneEmden Equation Journal of Applied Mathematical Sciences 26029552961
Saadatmandi A Ghasemi N and Effekhari A 2019 Numerical study of singular fractional LaneEmden type equation arising in astrophysics Journal of Astrophysics and Astronomy 403127 DOI: https://doi.org/10.1007/s12036-019-9587-0
Sahu P K and mallick B 2019 Approximate solution of fractional order LaneEmden type differential equation by orthonormal Bernoullis Polynomials International Journal of Applied and Computational Mathematics 589 DOI: https://doi.org/10.1007/s40819-019-0677-0
Taghavi A 2013 Spectral methods on the semiinfinite line MSc thesis Mathematics Department Simon Fraser University Burmaby British Columbia Canada 83pp
Waheed A and Zulgurnain S 2020 Solving a new design of nonlinear second order LaneEmden Pantograph delay differential model via Bernoulli collocation method The European Physical Science Journal135427
Copyright (c) 2024 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
