A novel Jacobi neural network method is proposed for solving linear differential-algebraic equations (DAEs) in the paper. First, Jacobi neural network is applied to derive the approximate solutions form of DAEs, and the loss function is constructed for DAEs based on single hidden layer Jacobi neural network structure. Then, we get the optimal output weights of Jacobi neural network by applying extreme learning machine algorithm. In particular, Legendre neural network method and Chebyshev neural network method which have been widely used by scholars are special cases of Jacobi neural network method, and the numerical results of the proposed method are better than these of Legendre neural network method and Chebyshev neural network method. Furthermore, Jacobi neural network method has higher accuracy compared with the approximate analytical methods, the numerical comparison results further show the feasibility and effectiveness of the proposed method for solving the DAEs.

本文提出了一种新的Jacobi 神经网络方法来求解线性微分代数方程(DAE)。首先应用Jacobi神经网络推导DAEs的近似解形式，并基于单隐层Jacobi神经网络结构为DAEs构建损失函数。然后，我们通过应用极限学习机算法得到 Jacobi 神经网络的最优输出权重。特别是学者们广泛使用的Legendre神经网络方法和Chebyshev神经网络方法是Jacobi神经网络方法的特例，所提方法的数值结果优于Legendre神经网络方法和Chebyshev神经网络方法. 此外，Jacobi 神经网络方法与近似解析方法相比具有更高的精度，