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A New Fourth-Order Compact Off-Step Discretization for the System of 2D Nonlinear Elliptic Partial Differential Equations

Published online by Cambridge University Press:  28 May 2015

R. K. Mohanty  and
Nikita Setia
R. K. Mohanty*
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India
Nikita Setia*
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India
*
Corresponding author. Email: rmohanty@maths.du.ac.in
Corresponding author. Email: mohantyranjankumar@gmail.com
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Abstract

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.

Keywords

65N0602.60.Lj02.70.BfTwo-dimensional nonlinear elliptic equationsoff-step discretizationfourth-order finite difference methods, normal derivativesconvection-diffusion equationPoisson equation in polar coordinatesNavier-Stokes equations of motion
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 1 , February 2012 , pp. 59 - 82
Copyright
Copyright © Global-Science Press 2012

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