Chebyshev Neural Network Method for Solving Delay-Integro-Differential-Algebraic Equations Based on Variable Transformation

Abstract

In this paper, a single hidden layer Chebyshev neural network based on extreme learning machine is proposed to solve linear and nonlinear delay-integro-differential-algebraic equations. Since the equations contain both delay and integral terms, which bring many difficulties to the numerical solution. This paper adopts a segmental solution to overcome the difficulties caused by the delay term and constructs a Chebyshev neural network, which can directly calculate the integral term through the Chebyshev polynomials. For linear delay-integral-differential-algebraic equations, we first segment the interval according to the delay term, construct a single hidden layer Chebyshev neural network, and combine the extreme learning machine optimization algorithm to obtain the optimal solution of each segment in turn, in which the optimal solution of the previous segment is used as the initial condition of the subsequent segment. For the nonlinear delay-integral-differential-algebraic equations, this paper first transforms the nonlinear equation into a linear equation using the variable transformation method, and then we simulate them using the same method. Numerical experiments show that the single hidden layer Chebyshev neural network based on the extreme learning machine can solve the linear model with high accuracy, and it is feasible and efficient to convert the nonlinear model into a linear model by using the variable transformation method for simulation.