基于GA-Chebyshev神经网络的一类分数阶微分方程的数值解

Numerical solution of a class of fractional differential equations based on GA-Chebyshev neural network

针对一类分数阶微分方程求数值解的问题,在切比雪夫神经网络的基础上,提出一种利用遗传算法优化切比雪夫神经网络的新方法,并通过2个算例验证了该方法的可行性和有效性。研究结果表明:与现有数值方法相比,采用改进的切比雪夫神经网络方法计算微分方程的数值解与准确解更为接近,误差较小。研究结论为分数阶微分方程中类似问题的求解提供了新思路。

Aiming at the problem of numerical solution of a class of fractional differential equations,a new method of optimizing Chebyshev neural network by genetic algorithm is proposed based on Chebyshev neural network.The feasibility and effectiveness of the method are verified by two examples.The results show that compared with the existing numerical methods,the numerical solution of the differential equation calculated by the improved Chebyshev neural network method is closer to the accurate solution and the error is smaller.The research conclusion provides a new idea for solving similar problems in fractional differential equations.