65 Numerical analysis -- 65M Partial differential equations, initial value and time-dependent initial-boundary value problems 65M25 Method of characteristics
Summary: ``In this article, we discuss the initial-boundary value problem of one-dimensional convection-dominated diffusion equations. By using the characteristic method and the ridge basis meshless method, we obtain the implicit scheme method and the explicit scheme method of the characteristic ridge basis meshless method. The numerical experiments show that the method has higher accuracy and is easy to calculate.''