分数阶Bagley-Torvik微分方程的初边值问题数值求解方法研究

Research on Numerical Solution Methods for Initial Boundary Value Problems of Fractional Order Bagley-Torvik Differential Equations

研究针对分数阶Bagley-Torvik微分方程的初边值问题,结合遗传算法(Genetic Algorithm,GA)和单输入Chebyshev神经网络(Chebyshev neural network,ChNN)搭建GA-ChNN神经网络,经过迭代后的最终权值即为微分方程的数值解。实验结果表明,研究优化的GA-ChNN神经网络误差绝对值更低,得到的数值解更为拟合微分方程的精确解。通过比较CPU执行时间可知,ChNN神经网络、GA-ChNN神经网络和算法优化的GA-ChNN神经网络的平均CPU执行时间分别为14.803s,1.026s和0.190s。通过与其他求解算法相比较,研究采用的优化GA-ChNN神经网络的绝对误差值最小且误差波动范围最小,其绝对误差最小值接近0.021,而误差波动范围在[0,0.2]之间,进一步验证了算法的优越性。

Research on the initial boundary value problem of fractional order Bagley-Torvik differential equations,combining genetic algorithm(GA)and single input Chebyshev neural network(ChNN)to construct a GA-ChNN neural network.The final weight after iteration is the numerical solution of the differential equation.The experimental results indicate that the optimized GA-ChNN neural network has a lower absolute error value,and the numerical solution obtained is more accurate in fitting the differential equation.By comparing the CPU execution time,it can be seen that the average CPU execution time of ChNN neural network,GA-ChNN neural network,and algorithm optimized GA-ChNN neural network are 14.803s,1.026s,and 0.190s,respectively.Compared with other solving algorithms,the optimized GA-ChNN neural network used in the study has the smallest absolute error value and the smallest error fluctuation range.Its absolute error minimum value is close to 0.021,and the error fluctuation range is between[0,0.2],further verifying the superiority of the algorithm.