Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

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 alg orithm for the solution of different problems is investigated. Meanwhile, the convergence analysis based on the resulting statistical data is also discussed. 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): a1,0 (x)u 00(x) +a1,1 (x)u 0 (x) + a1,2 (x)u1(x) +a1,3 (x)u 00 (x) + a1,4 (x)u 0 (x) +a1,5 (x)u2(x) + G1 (x,u1(x),u2(x)) = f1 (x), a2,0 (x)u 00(x) +a2,1 (x)u 0(x) + a2,2 (x)u2(x) +a2,3 (x)u 00(x) + a2,4 (x)u 0(x) +a2,5 (x)u1(x) + G2 (x,u1(x),u2(x)) = f2 (x),