Open AccessNew Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds
Author(s) -
W. M. AbdElhameed,
E. H. Doha,
Y. H. Youssri
Publication year - 2013
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2013/542839
Subject(s) - mathematics , chebyshev polynomials , algebraic equation , chebyshev iteration , collocation (remote sensing) , orthogonal collocation , boundary value problem , spectral method , wavelet , nonlinear system , collocation method , mathematical analysis , chebyshev filter , chebyshev equation , differential equation , orthogonal polynomials , classical orthogonal polynomials , computer science , ordinary differential equation , physics , quantum mechanics , machine learning , artificial intelligence
This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. Convergence analysis and some specific numerical examples are discussed to demonstrate the validity and applicability of the proposed algorithms. The obtained numerical results are comparing favorablywith the analytical known solutions
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