Numerical Method Of Volterra Integral Equation Based On Wayelet Neural Network

Integral equations are an important part of modern mathematics research,and its application field is widely penetrated in many disciplines such as physics,biology,chemistry and so on,and many practical problems can be reduced to the problem of integral equations to solve.While Volterra integral equation occupies an important position among integral equations,but due to its non-analytic or analytic solution form,the research of numerical solutions has become the focus of scholars.In recent years,the neural network technology continues to mature,and the wavelet neural network is formed as the neural network matures.The wavelet neural network has gradually developed.It not only has the advantages of fast operation speed and strong anti-interference ability,but also has the advantages of wavelet transform,which makes the wavelet neural network has better performance in function approximation,so this paper constructs a wavelet neural network model to solve the second kind of Volterra integral equation.Firstly,this article briefly describes the theoretical basis of artificial neural networks and wavelet neural networks.Secondly,a single hidden layer wavelet neural network model optimized by gradient descent algorithm is constructed,at the same time the convergence of the model is proved,and we can use the model to solve the numerical solution of the second kind of Volterra integral equation.Finally,a new double hidden layer wavelet neural network model is constructed.By introducing the Lyapunov function,the convergence of the double hidden layer wavelet neural network model is proved,The nu-merical examples of Volterra integral equations of the second kind are used to verify the feasibility and effectiveness of this method.