Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm

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 Kortewegde 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.

An improved data-free surrogate model for solving partial differential equations using deep neural networks

“…This approach uses conditional Karhunen–Lo ve expansion (cKLE) to minimize the PDE residuals and approximate the observed parameters and states. Ahalpara 14 developed a surrogate model for solving the Korteweg–de Vries (KdV) equation using a genetic algorithm. A random forest regression model was introduced by Wang et al 15 to predict the Reynolds stresses in the flow over periodic hills.…”