Appl. Math. Inf. Sci. 8, No. 1, 235-248 (2014) 235 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.12785/amis/080129 Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems Omar Abu-Arqub 1,∗ , Zaer Abo-Hammour 2 and Shaher Momani 3,∗ 1 Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan 2 Department of Mechatronics Engineering, Faculty of Engineering, University of Jordan, Amman 11942, Jordan 3 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan Received: 1 Jun. 2012, Revised: 9 Sep. 2012, Accepted: 10 Sep. 2012 Published online: 1 Jan. 2014 Abstract: In this paper, a numerical algorithm, based on the use of genetic algorithm technique, is presented for solving a class of nonlinear systems of second-order boundary value problems. In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraints boundary condtions, and is then solved using continuous genetic algorithm. In general, the proposed technique uses smooth operators and avoids sharp jumps in the parameter values. The applicability, efficiency, and accuracy of the proposed algorithm for the solution of different problems is investigated. Meanwhile, the convergence analysis based on the resulting statistical data is also discussed. Keywords: Continuous genetic algorithm, second-order boundary value problems, finite difference method 1 Introduction Systems of second-order boundary value problems (BVPs) occur frequently in applied mathematics, engineering, theoretical physics, biology and so on [1, 2, 3]. If the systems of second-order BVPs cannot be solved analytically because, generally, the solution cannot be exhibited in a closed form even when it exists, which is the usual case, then recourse must be made to numerical and approximate methods. Many classical numerical methods used with second-order initial value problems cannot be applied to second-order BVPs. We all know that the finite difference method can be used to solve linear second-order BVPs, but it can be difficult to solve nonlinear second-order BVPs. Furthermore, the finite difference method requires some major modifications that include the use of some root-finding technique while solving nonlinear second-order BVPs. For a nonlinear system of second-order BVPs, there are few valid methods to obtain numerical solutions. In this paper, we apply the continuous genetic algorithm (CGA) (The term ”continuous” is used to emphasize that the continuous nature of the optimization problem and the continuity of the resulting solution curves) for the solution of the following nonlinear system of second-order BVPs [4]: a 1,0 (x) u ′′ 1 (x) +a 1,1 (x) u ′ 1 (x)+ a 1,2 (x) u 1 (x) +a 1,3 (x) u ′′ 2 (x)+ a 1,4 (x) u ′ 2 (x) +a 1,5 (x) u 2 (x)+ G 1 (x, u 1 (x),u 2 (x)) = f 1 (x) , a 2,0 (x) u ′′ 2 (x) +a 2,1 (x) u ′ 2 (x)+ a 2,2 (x) u 2 (x) +a 2,3 (x) u ′′ 1 (x)+ a 2,4 (x) u ′ 1 (x) +a 2,5 (x) u 1 (x)+ G 2 (x, u 1 (x),u 2 (x)) = f 2 (x) , (1) subject to the boundary conditions u 1 (a)= α 1 ,u 1 (b)= β 1 , u 2 (a)= α 2 ,u 2 (b)= β 2 , (2) where a ≤ x ≤ b, α k ,β k , k = 1, 2 are real finite constants, G 1 ,G 2 are nonlinear functions of u 1 ,u 2 , and f 1 ,f 2 and a 1,i ,a 2,i , i = 0, 1, 2, 3, 4, 5 are continuous functions on [a, b]. The previous studies for system (1) and (2) can be summarized as follows: in [5], the authors have discussed ∗ Corresponding author e-mail: o.abuarqub@bau.edu.jo, s.momani@ju.edu.jo c  2014 NSP Natural Sciences Publishing Cor.