TITLE:
Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm
AUTHORS:
Dilip P. Ahalpara
KEYWORDS:
Sniffer Technique, Genetic Algorithm, Numerical Solution of ODE, Evolutionary Computation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.7,
June
30,
2015
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.