A New Fourth-Order Compact Off-Step Discretization for the System of 2D Nonlinear Elliptic Partial Differential Equations
R. K. Mohanty 1*, Nikita Setia 21 Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India.
Received 29 December 2011; Accepted (in revised version) 8 February 2012
Available online 10 February 2012
This paper discusses a new fourth-order compact off-step discretization for the solution of a system of two-dimensional nonlinear elliptic partial differential equations subject to Dirichlet boundary conditions. New methods to obtain the fourth-order accurate numerical solution of the first order normal derivatives of the solution are also derived. In all cases, we use only nine grid points to compute the solution. The proposed methods are directly applicable to singular problems and problems in polar coordinates, which is a main attraction. The convergence analysis of the derived method is discussed in detail. Several physical problems are solved to demonstrate the usefulness of the proposed methods.
AMS subject classifications: 65N06
PACS: 02.60.Lj; 02.70.Bf
Key words: Two-dimensional nonlinear elliptic equations, off-step discretization, fourth-order finite difference methods, normal derivatives, convection-diffusion equation, Poisson equation in polar coordinates, Navier-Stokes equations of motion.
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