Application of Collocated Legendre Expansions on Some Ibvps
Ghorbani Mehrzada, Nafisinia Yunesb, Ghorbani jafarbeigloo Royac
aDept. of Maths., Velayat Univ., Iranshahr / Iran.
bDept.of Maths., Suppl. Edu., Islamic Azad Univ., Zahedan Branch/Zahedan / Iran.
cDept.of Math., Khajeh Nasir Toosi University of Technology, Tehran/Iran.
Abstract:The aim of this paper is numerical solution of some IBVPs with various boundary conditions. Here, we approximated some second order IBVPs using Legendre special function expansion. Then, we use Legendre polynomials on the interval [-1, 1] as the basis functions (i. e. shape or approximation functions) for collocation method. We also evaluate conditions that can give better approximations, then present some examples of different boundary conditions and finally our approximate solutions are compared with its analytic solution.
[Ghorbani Mehrzad, Nafisinia Yunes,Ghorbani jafarbeigloo Roya. Application of collocated Legendre expansions on some IBVPs. Life Sci J 2013;10(1):1004-1009] (ISSN:1097-8135). http://www.lifesciencesite.com. 6
Keywords: collocation method, second order IBVP, Legendre polynomials, nodal distribution.