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Arqub, Omar Abu; Abo-Hammour, Zaer; Momani, Shaher; Shawagfeh, Nabil

Solving singular two-point boundary value problems using continuous genetic algorithm. (English) Zbl 1261.34018

Abstr. Appl. Anal. 2012, Article ID 205391, 25 p. (2012).
Summary: A continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses some advantages: it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward and simple.

Cited in 20 Documents

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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\textit{O. A. Arqub} et al., Abstr. Appl. Anal. 2012, Article ID 205391, 25 p. (2012; Zbl 1261.34018)
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