Abstract
In this paper, we present a new algorithm to find exact and approximate analytical solutions of singular two-point boundary-value problems (BVPs) based on Bernstein operational matrix of differentiation. Different from other numerical techniques, Bernstein polynomials and their properties are employed for deriving a general procedure for forming this matrix. The proposed method can be applied to linear and nonlinear problems. The scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed method.
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