Gongcheng Shuxue Xuebao. Chinese Journal of Engineering Mathematics (Gongcheng Shuxue Xuebao) (20130101), 30, no.~5, 721-730. ISSN: 1005-3085 (print).
Subject
65 Numerical analysis -- 65M Partial differential equations, initial value and time-dependent initial-boundary value problems 65M70 Spectral, collocation and related methods
This paper proposes a meshless method using a new ridge basis function, which is applied to solve convection-dominated diffusion problems in the collocation framework. The existence and uniqueness of the numerical solutions are proved. The numerical experiments show that the new method is very efficient, especially for elimination of numerical oscillations.