关键词: 变分优化, 微分方程, 权余量方法, 粒子群算法

Abstract: In view of studying variational problems and finding the principle of transformation in the issue of differential equations and variational problems，the solution of combining right surplus method of differential equations with standard particle swarm algorithm to find a better algorithm for variational optimization problems.In the right surplus calculation method，the equations are transformed into the approximate objective function and the minimum variational problem，the standard particle swarm algorithm is used to solve them.On the dependent the powers of variable are high times in the variational problem，it can directly use the modified algorithm to solve it.On the dependent the powers of variable are one time，need to respectively square on the left and right equation，then it is converted to minimum variational problem and solving.And then the algorithm is tested with an variational problem example and founding that the improved algorithm is easy，calculation process is simple，the result is good.And the number of the base of the approximate objective function takes three or four times to compare，for specific issues，it should be better adapted to practical problem of selecting the number of times，and then getting better results.From the theoretical analysis，the algorithm is also feasible and it has practical significance.

Key words: variational optimization, differential equations, right surplus method, Particle Swarm Optimization algorithm