Numerical Solutions Of Several Telegraph Equations Based On Meshless Methods

The main idea of this thesis is to get the numerical solution of a kind of hyperbolic telegraph equation using the meshless methods. Telegraph equations are important partial differential equations which are applied in various fields, such as electricity, mechanics of elasticity, fluid mechanics, acoustics, microwave technology and so on. Many researchers have been given much attention to the telegraph equations. And telegraph equations are also considered as an spacial partial differential equations, except a few cases, there is no analysis solution of the most, just can get the numerical solution through the numerical methods, so the research of numerical solution for the hyperbolic telegraph equation has very important significance.Meshless method is a kind of recently proposed novel numerical tool for solving partial differential equations which have gained popularity used in fluid mechanics, ma-terial mechanics, solid mechanics and mechanical engineering during the two decades. Meanwhile, more and more experts and scholars make attention to it. The most signif-icant characteristic of meshless method is that it doesn’t need mesh, compared with the traditional method, meshless methods get rid of the initialization of the mesh and the con-straints of mesh reconstruction, ensure the precision of solution, and greatly reduces the computation complexity. The meshless methods do not need the grid very much,and it can avoid the grid distorted and twisted problem. It can give expression to particular advan-tages in some areas, which the finite element method and the boundary method could not solve. Although, compared with the traditional method, the theories of meshless are not fully development, meshless method is also a kind of very promising numerical method and have important research value.This paper performs a meshless collocation method based on the interpolation of radial basis functions(RBFs) for solving some telegraph equations, where the founda-tion is radial basis function and its radial basis function interpolation. In addition, the paper mainly introduce Kansa’s Method, the Method of Particular Solutions(MPS), and use the two methods to solve some hyperbolic telegraph equations, including one-dimensional(1D), two-dimensional(2D), three-dimensional(3D) linear telegraph equation-s, nonlinear telegraph equations and nonhomogeneous problems. Through the numerical comparison, conformed the effectiveness.