Abstract
We present an approximate solution depending on collocation method and Bernstein polynomials for numerical solution of a singular nonlinear differential equations with the mixed conditions. The method is given with two different priori error estimates. By using the residual correction procedure, the absolute error might be estimated and obtained more accurate results. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. AMS Subject Classification: 15B99, 14F10
Highlights
In this work, we consider the singular problems of the type y′′(x) + p(x)y′(x) + q(x)y(x) = g(x) 0 < x ≤ 1, (1)subject to the conditionsReceived: January 28, 2015 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.euM.H.T
We use Bernstein operational matrix to solve a linear and nonlinear singular boundary value problems it was solved by wavelet analysis method by [1]
We report our numerical solutions its become more accurate as we can see only small number of Bernstein polynomial basis functions are needed to get the approximate solution in full agreement with the exact solution up to 10 digits
Summary
Nasab and Kilicman employed Wavelet analysis method for solving linear and nonlinear singular boundary value problems [1]. Bataineh and Ishak Hashim used Legendre Operational matrix to approximate solution of two points BVPs [2]. Pandey and kumar solved Lane-Emden type equations by Bernstein operational matrix [4]. Yousefi employed operational matrices of Bernstein polynomials and their applications to solve Bessel differential equation [5]. We use Bernstein operational matrix to solve a linear and nonlinear singular boundary value problems it was solved by wavelet analysis method by [1].
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