Numerical Solution of Tenth Order Boundary Value Problems by Galerkin Method with Quintic B-splines

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Year:
2014
Type of Publication:
Article
Keywords:
Absolute Error, Galerkin Method, Quintic B-Splines, Tenth Order Boundary Value Problem, Quasilinearization
Authors:
K. N. S. Kasi Viswanadham; Sreenivasulu Ballem
Journal:
IJISM
Volume:
2
Number:
3
Pages:
288-294
Month:
May
Abstract:
In this paper, we present a finite element method involving Galerkin method with quintic B-splines as basis functions to solve a general tenth order boundary value problem. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet boundary conditions, Neumann boundary conditions, second order derivative boundary conditions, third order derivative boundary conditions, and fourth order derivative types of boundary conditions are prescribed. The proposed method was applied to solve several examples of tenth order linear and nonlinear boundary value problems. The solution of a nonlinear boundary value problem has been obtained as the limit of a sequence of solution of linear boundary value problems generated by quasilinearization technique. The obtained numerical results are compared with the exact solutions available in the literature.

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