new solutions for singular lane-emden equations arising in astrophysics based on shifted ultraspherical operational matrices of derivatives

نویسنده

abd- elhameed waleed m. ,youssri youssri ,doha eid h.

منبع

computational methods for differential equations - 2014 - دوره : 2 - شماره : 3 - صفحه:171 -185

فایل تمام متن

چکیده

in this paper, the ultraspherical operational matrices of derivatives are constructed. based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear lane-emden type singular initial value problems. the basic idea behind the suggested algorithms is built on transforming the equations with their initial conditions into systems of linear or nonlinear algebraic equations which can be solved by using suitable numerical solvers. the legendre and rst and second kind chebyshev operational matrices of derivatives can be deduced as special cases of the constructed operational matrices. for the sake of testing the validity and applicability of the suggested numerical algorithms, three illustrative examples are presented.

کلیدواژه

ultraspherical polynomials ,operational matrix of derivatives ,laneemden equations ,isothermal gas spheres equation

آدرس

university of jeddah, faculty of science, department of mathematics, saudi arabia. cairo university, faculty of science, department of mathematics, egypt, cairo university, faculty of science, department of mathematics, egypt, cairo university, faculty of science, department of mathematics, egypt

پست الکترونیکی

eiddoha@sci.cu.edu.eg

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