摘要： 针对传统变分法求解困难的问题，提出一种变分优化问题的近似解法。根据最小二乘近似解法的简便性与粒子群优化算法参数少的特性，在最小二乘近似解法的求解过程中引入粒子群优化算法，并给出求解流程。数值仿真实验结果表明，该算法计算过程简单，优化效果较好。

关键词: 变分法, 最小二乘法, 粒子群优化, 变分优化, 微分方程

Abstract: For the problem of the traditional variational method to solve difficultly, the approximate solution of a variational optimization problem is proposed. Combining the simplicity of least squares approximate solution with the parameters less of the particle swarm optimization algorithm, it introduces the particle swarm optimization algorithm in the process of solving the least squares approximate solution, and gives the solution process. The numerical simulation results show that the algorithm is a simple calculation, and its optimization effect is better.

Key words: variational method, least squares method, Particle Swarm Optimization(PSO), variational optimization, differential equations

中图分类号: 

• TP301.6