Improved PSO Research for Solving the Inverse Problem of Parabolic Equation

Abstract

Parameter identification problem has important research background and research value, has become in recent years inverse problem of heat conduction of top priority. This paper studies the Parabolic Equation Inverse Problems of parameter identification problem, and applies PSO to solve research. Firstly, this paper establishes the model of the inverse problem of partial differential equations. The content and classification of the inverse problem of partial differential equations are explained. Frequently, the construction and solution of the finite difference method for parabolic equations are studied, and two stable schemes for one dimensional parabolic equation are given. And two numerical simulations were given. Partial differential equation discretization was with difference quotient instead of partial derivative. The partial differential equations with initial boundary value problem into algebraic equations, and then solving the resulting algebraic equations. Then, the basic principles of PSO and its improved algorithms are studied and compared. Particle swarm optimization algorithm program implementation. Finally, the Parabolic Equation Inverse Problems of particle swarm optimization algorithm performed three simulations. We use a set of basis functions gradually approaching the true solution, selection of initial value. The reaction is converted into direct problem question, then use difference method Solution of the direct problem. The solution of the problem with the additional conditions has being compared. The reaction optimization problem is transformed into the final particle swarm optimization algorithm to solve. Verify the Parabolic Equation Inverse Problems of particle swarm optimization algorithm correctness and applicability.