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

Abstract

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.

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

“…However, the reader is referred to [31][32][33][34][35] in order to know more details about these methods, including their types and history, their motivation for use, their characteristics, and their applications. On the other hand, the numerical solvability of other version of differential equations and other related equations can be found in [36][37][38][39][40][41][42][43] and references therein.…”

“…Similar to the previous procedure and discussions that used in Application 5.1, the FPS solution and the residual function for Equations (42) and (43) will take, respectively, the following form:…”

“…Thus, based on the initial guess approximation and the form of terms of Equation (42) taking into account the form of Equations (46) and (47), it easy to see that 0, 1, 2, 3, …. Therefore, according to Equation (44) a new discretized form of FPS solution for Equations (42) and (43) can be obtained and expressed as: (49) and hence the , 0 -truncated series approximation of can formulated as:…”

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models

“…The aim of this study is to step further in this domain by exploring and exploiting the strength of soft computing framework (SCF) to determine the solution of systems of nonlinear equation without prior knowledge of biased initial guess or weights. The soft computing techniques based on genetic algorithms and swarming intelligence has been used extensively for different applications such as Van-der-Pol oscillatory systems (Khan et al 2015), reliable feature selection for Arabic text summarization (Al-Zahrani et al 2015), effective navigation of mobile robot in unknown environment(Algabri et al 2014), robust feature selection and classification (Nekkaa and Boughaci 2015), fuel ignition model in combustion theory (Raja 2014), change detection mechanism in synthetic aperture radar images (Li et al 2015), optimization of multirate quadrature mirror filter bank (Baicher 2012), integrated process planning and scheduling problems (Li et al 2014), thin film flow of third grade fluids (Raja et al 2014), Troesch’s problem (Raja 2014), second order system of boundary value problems (Arqub and Abo-Hammour 2014; Abu-Arqub et al 2014), prediction of linear dynamical systems (Abo-Hammour et al 2013), Jeffery-Hamel Flow in the presence of high magnetic field (Raja and Samar 2014), Painlevé equations (Raja et al 2015), modeling of electrical conducting solids (Raja et al 2016), nanofludics problems (Raja et al 2016), Riccati fractional differential equations (FrDEs) (Raja et al 2015), real time cross layer optimization (Elias et al 2012) and Bagley-Torvik FrDEs (Raja et al 2011). These are the motivating factors for the authors to explore in this domain.…”

Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

“…Also, for numerical solvability of different categories of two-point, second-order BVPs one can consult the Refs. [22,23].…”