Genetic Algorithm For Solving Ordinary And Partial Differential Equations

Genetic algorithm brings up a common frame to solve complex system problems, such as non-linear, multi-model, multi-objective and so on. It does not depend on the specific areas of problems and has been applied to many technological areas like functional optimization, combination optimization, auto-control, machine learning. Many problems in natural science and engineering technology could be expressed in a form of differential equations, while it is often difficult to solve that. This article presented a method to transform the problem of solving differential equations to the problem of optimization according to least square principle and some examples were solved to prove it feasible.The paper firstly analyzes the background and meanings of the research work and summarizes the research present situations home and abroad. At the same time, several methods solving differential equations now have been pointed out. Based on above, to solve differential equations with genetic algorithm is established as the main research contents.Secondly, the basic of genetic algorithm is elaborated and its characteristics and applications is detailed, meanwhile it also introduces the tools of genetic algorithm in MATLAB. Thirdly, based on above, genetic algorithm applying to solve differential equations is researched. How to transform the solving problem to optimization problem and how to construct analytical solution is proposed. Also it gives a method to set some parameters through the process solving some examples and the feasibility of the method is illustrated by putting it into solving those examples.At last, the research work is summarized and expected.