Abstract:

Particle swarm optimization algorithm is combined with difference schemes to solve a class of singularly perturbed convection-diffusion problems on Bakhvalov-Shishkin mesh. The particle swarm optimization algorithm is used to optimize the mesh parameter in Bakhvalov-Shishkin mesh, and the objective function for finding minimum value of the error norm is constructed. Two numerical examples are calculated. The experimental results show that the particle swarm optimization algorithm can obtain better numerical results than the fixed mesh parameter, and the numerical results are convergent, which verifies the effectiveness and superiority of this method.

Key words: particle swarm optimization algorithm, singular perturbation, Bakhvalov-Shishkin mesh, mesh parameter

摘要：

针对一类奇异摄动对流扩散问题，将粒子群算法与差分格式相结合，在Bakhvalov-Shishkin网格上进行求解。对于Bakhvalov-Shishkin网格中的网格参数，采用粒子群算法进行优化，构造了求误差范数最小值的目标函数。对两个算例进行了数值计算，实验结果表明，与选择固定的网格参数相比，采用粒子群算法计算能得到更好的数值结果，并且数值结果具有收敛性，验证了该方法的有效性和优越性。

关键词: 粒子群算法, 奇异摄动, Bakhvalov-Shishkin网格, 网格参数