Solving nonlinear elliptic partial differential equations in 2D using oscillatory radial basis functions collocation method

Abstract

Oscillatory radial basis functions collocation method (ORBF-CM) has been proven to be an effective meshless numerical method for solving various linear elliptic partial differential equations (PDEs). In general, solving nonlinear PDEs is a daunting task. In this paper, we propose a numerical method for solving nonlinear PDEs using ORBF-CM. While solving nonlinear problems, trust-region-reflective least-square and Picard iteration methods have been used. Numerical experiments presented in this paper clearly verify that our proposed method is highly accurate.

Keywords

• Oscillatory radial basis functions
• Collocation method
• Nonlinear partial differential equations
• Trust-region-reflective least-square method
• Picard iteration method
• Particular solutions