Localized oscillatory radial basis functions collocation method for solving elliptic partial differential equations in 2D

Abstract

In recent years, localized methods are proven to be very effective for solving various types of problems in scientific computing. Many researchers have successfully implemented localized approaches to solve large-scale problems. Oscillatory radial basis functions collocation method, a global method, is a meshless numerical method in the literature. The novelty of this article is to address the computational efficiency issues of the oscillatory radial basis functions collocation method using a localized approach for solving elliptic partial differential equations in 2D. We carry out a number of experiments to validate our proposed numerical scheme. Numerical results clearly demonstrate that our scheme is highly accurate and computationally efficient.