TY - JOUR
T1 - A New Fourth-Order Compact Off-Step Discretization for the System of 2D Nonlinear Elliptic Partial Differential Equations
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 59
EP - 82
PY - 2018
DA - 2018/02
SN - 2
DO - http://doi.org/10.4208/eajam.291211.080212a
UR - https://global-sci.org/intro/article_detail/eajam/10867.html
KW - 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.
AB - <p style="text-align: justify;">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.</p>