Localized method of particular solutions using polynomial basis functions for solving two-dimensional nonlinear partial differential equations

Abstract

The localized method is one of the popular approaches in solving large-scale problems in science and engineering. In this paper, we implement the localized method of particular solutions using polynomial basis functions for solving various nonlinear problems. To validate our proposed numerical method, we present four numerical examples in regular and irregular domains which are solved by using localized method of particular solution with polynomial basis functions. We compared our numerical method with localized method of particular solutions using multiquadric radial basis function and numerical results clearly show that our numerical method is highly accurate, efficient, and outperformed the method using multiquadric radial basis function.

Keywords

• Nonlinear problems
• Radial basis functions
• Particular solutions
• Polynomial basis functions
• Localized method of particular solutions
• Multiquadric