Abstract
A novel heuristic technique has been developed for solving Ordinary Differential Equation (ODE) numerically under the framework of Genetic Algorithm (GA). The method incorporates a sniffer procedure that helps carry out a memetic search within the solution domain in the vicinity of the currently found best chromosome. The technique has been successfully applied to the Korteweg- de Vries (KdV) equation, a well-known nonlinear Partial Differential Equation (PDE). In the present study we consider its solution in the regime of solitary waves, or solitons that is first used to convert the PDE into an ODE. It is then shown that using the sniffer technique assisted GA procedure, numerical solution has successfully been generated quite efficiently for the one-dimensional ODE version of the KdV equation in space variable (x). The technique is quite promising for its applications to systems involving ODE equations where analytical solutions are not directly available.
Highlights
Dynamical systems involving Ordinary Differential Equations (ODEs) occur in many branches of science, including Physics, Chemistry, Biology, Econometrics etc
Using various forms for the template curves, different regimes of solutions are obtained by the Genetic Algorithm (GA) pro
It has been shown that the sniffer technique assisted Genetic Algorithm approach is quite useful in solving onedimensional Kortewegde Vries (KdV) equation
Summary
Dynamical systems involving Ordinary Differential Equations (ODEs) occur in many branches of science, including Physics, Chemistry, Biology, Econometrics etc. Considerable work has been reported in the literature for obtaining numerical solution for ODE equations. John Butcher [2] describes a variety of numerical methods for solving differential equations. Tsoulos and Lagaris [3] have used grammatical evolution method for solving ODE equations. A variety of numerical techniques have been used in the past for solving ODEs, including use of Runge Kutta method, Predictor Corrector based method by Lambert [4], meshless Radial Basis functions by Fasshauer [5], Artificial Neural Network with a regression based algorithm by Lagaris et al [6]. Inference of pertinent system equations of ODE type have been tried out by using the
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