Numerical Solutions Of Nonhomogeneous Telegraph Equation Based On Mesh-Less Methods

Nonhomogeneous telegraph equation, a class of special time dependent nonlinear partial differential equation, has been widely applied in electrical, optical, acoustic and microwave technology, and other fields. In most cases, it is difficult to get the analytical solution, and the numerical solution is studied instead. So the study of the numerical solution of the nonhomogeneous telegraph equation has extremely important theory sig-nificance and application value.This article mainly studies the meshless method of particular solution for the nonho-mogeneous telegraph equation. Firstly, the temporal derivative is discretized using finite difference method. Then the function and the spatial derivative are approximated by the chosen radial basis functions. Finally, the numerical solution can be achieved by solving the collocation matrix layer by layer.The structure of this article is arranged as follows:In introduction, the research background, research methods, present research situation of the considered question and the main research work of this article are introduced respectively. In the second chapter, a detailed discussion on the radial basis function interpolation theory is given after the relevant concepts of the radial basis function. The third chapter introduces three kinds of radial basis function based on meshless methods. In the fourth chapter, the meshless method of particular solution is used to solve the nonhomogeneous telegraph equation and numerical examples shows efficiency and stability of the presented method. At last, the summary and follow-up research outlook is listed.