Solving the elliptic Monge-Ampere equation by Kansa's method

摘要

The elliptic Monge-Ampere equation is a fully nonlinear partial differential equation, which originated in geometric surface theory and has been widely applied in dynamic meteorology, elasticity, geometric optics, image processing and others. The numerical solution of the elliptic Monge-Ampere equation has been a subject of increasing interest recently. In this paper, Kansa's method (with multiquadric basis functions) is introduced and used to solve numerically the Monge-Ampere equation. Kansa's method is a meshfree method which uses the combination of some radial basis functions (RBFs) to approximate the solution of the partial differential equation. We prove the classical consistency of the Kansa's method for the elliptic Monge-Ampere equation. Finally, we also present some numerical experiment to demonstrate the effectiveness of Kansa's method for the elliptic Monge-Ampere equation.