Solving Second-Order Nonlinear Ordinary Differential Equations Based on Improved Genetic Algorithm

Abstract

AbstractIn scientific research and production, researchers often use ordinary differential equations as mathematical modeling tools. Ordinary differential equations are often used to describe the laws of dynamic systems and have been widely used in many fields. However, there are many types of ordinary differential equations, and they are affected by many factors. In order to solve many problems encountered in the process of finding ordinary differential equation models, this paper takes the second-order nonlinear ordinary differential equations as the object to explore the improved genetic algorithm in solving the second-order nonlinear ordinary differential equations. This article first summarizes the status quo of the derivation of ordinary differential equations at home and abroad, and outlines the basic theories of genetic algorithms and ordinary differential equations. On this basis, combined with improved genetic algorithms to solve ordinary differential equations. This article systematically explained the steps of improving the genetic algorithm to solve the nonlinear equations, and used comparative analysis method, observation method and other research methods to carry out experimental research on the subject of this article. Studies have shown that when the number of individuals in the population is too large, the search space will also increase, which will directly cause the algorithm to slow down and the efficiency of the algorithm will also deteriorate.KeywordsGenetic algorithmSecond-order nonlinearityOrdinary differential equationsSolution analysis