A new compact high order off-step discretization for the system of 2D quasi-linear elliptic partial differential equations

Advances in Difference Equations

Ranjan K Mohanty¹  Nikita Setia² 

[1] Department of Applied Mathematics, Faculty of Mathematics and Computer Science, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, India;Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India

关键词: quasi-linear elliptic equations;    fourth-order finite difference methods;    convection-diffusion equation;    Burger’s equation;    Poisson’s equation in polar coordinates;    Navier-Stokes equations of motion;   

DOI  :  10.1186/1687-1847-2013-223

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A new fourth-order difference method for solving the system of two-dimensional quasi-linear elliptic equations is proposed. The difference scheme referred to as off-step discretization is applicable directly to the singular problems and problems in polar coordinates. Also, new fourth-order methods for obtaining the first-order normal derivatives of the solution are developed. The convergence analysis of the proposed method is discussed in details. The methods are applied to many physical problems to illustrate their accuracy and efficiency. MSC: 65N06.

【 授权许可】

CC BY