Abstract
In this paper, a collocation method based on Laguerre wavelets is proposed for the numerical solutions of linear and nonlinear singular boundary value problems. Laguerre wavelet expansions together with operational matrix of integration are used to convert the problems into systems of algebraic equations which can be efficiently solved by suitable solvers. Illustrative examples are given to demonstrate the validity and applicability of this technique, and the results have been compared with the exact solutions.
Highlights
Singular boundary value problems (BVPs) for ordinary differential equations occur frequently in the fields of engineering and science such as gas dynamics, nuclear physics, atomic structures and chemical reactions [ ]
The purpose of this paper is to develop a Laguerre wavelets collocation method as an alternative method to solve singular two-point boundary value problems of the form [ ]
Numerous research work has been invested to study the singular BVPs of the form ( )( )
Summary
Singular boundary value problems (BVPs) for ordinary differential equations occur frequently in the fields of engineering and science such as gas dynamics, nuclear physics, atomic structures and chemical reactions [ ]. Orthogonal polynomial methods have seen significant achievements in dealing with singular boundary value problems, for example, Legendre polynomials [ ], Chebyshev polynomials [ ], Bernstein polynomials [ ], Laguerre polynomials [ ], Bessel polynomials [ ], Hermite polynomials [ ], and Bernoulli polynomials [ ]. Note that these polynomials are supported on the whole interval. One advantage of wavelet analysis is the ability to perform a local analysis This characteristic of time-frequency localization can overcome the defect and allows us to obtain very accurate numerical solutions
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