Premium
An iterative meshfree method for the elliptic monge–ampère equation in 2D
Author(s) -
Liu Zhiyong,
He Yinnian
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21849
Subject(s) - mathematics , partial differential equation , elliptic partial differential equation , poisson's equation , elliptic curve , nonlinear system , iterative method , mathematical analysis , monge–ampère equation , parabolic partial differential equation , first order partial differential equation , mathematical optimization , physics , quantum mechanics
The elliptic Monge–Ampère 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–Ampère equation has been a subject of increasing interest recently. In this article, we provide an iterative meshfree method for the elliptic Monge–Ampère equation. The nonlinear equation is simplified as series of Poisson equations with the iterative sequence. Then, the Kansa's method is used to solve these linear equations. We prove the convergence of this method. We also present some numerical experiments to demonstrate the theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1507–1517 , 2014