A New Fourth-Order Compact Off-Step Discretization for the System of 2D Nonlinear Elliptic Partial Differential Equations
Year: 2012
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 1 : pp. 59–82
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.291211.080212a
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 1 : pp. 59–82
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: 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.
-
Cubic spline approximation based on half-step discretization for 2D quasilinear elliptic equations
Mohanty, R. K. | Kumar, Ravindra | Setia, NikitaInternational Journal for Computational Methods in Engineering Science and Mechanics, Vol. 22 (2021), Iss. 1 P.45
https://doi.org/10.1080/15502287.2020.1849444 [Citations: 0] -
High-resolution half-step compact numerical approximation for 2D quasilinear elliptic equations in vector form and the estimates of normal derivatives on an irrational domain
Priyadarshini, Ishaani | Mohanty, R. K.Soft Computing, Vol. 25 (2021), Iss. 15 P.9967
https://doi.org/10.1007/s00500-020-05505-3 [Citations: 7] -
A high accuracy compact semi-constant mesh off-step discretization in exponential form for the solution of non-linear elliptic boundary value problems
Manchanda, Geetan | Mohanty, R. K. | Khan, ArshadJournal of Difference Equations and Applications, Vol. 27 (2021), Iss. 4 P.531
https://doi.org/10.1080/10236198.2021.1920936 [Citations: 3] -
A Novel Numerical Algorithm of Numerov Type for 2D Quasi-linear Elliptic Boundary Value Problems
Mohanty, R. K. | Kumar, RavindraInternational Journal for Computational Methods in Engineering Science and Mechanics, Vol. 15 (2014), Iss. 6 P.473
https://doi.org/10.1080/15502287.2014.934488 [Citations: 6] -
A new off-step high order approximation for the solution of three-space dimensional nonlinear wave equations
Mohanty, R.K. | Gopal, VenuApplied Mathematical Modelling, Vol. 37 (2013), Iss. 5 P.2802
https://doi.org/10.1016/j.apm.2012.06.021 [Citations: 22] -
A class of new implicit compact sixth-order approximations for Poisson equations and the estimates of normal derivatives in multi-dimensions
Mohanty, R.K. |Results in Applied Mathematics, Vol. 22 (2024), Iss. P.100454
https://doi.org/10.1016/j.rinam.2024.100454 [Citations: 0] -
A new high accuracy two-level implicit off-step discretization for the system of two space dimensional quasi-linear parabolic partial differential equations
Mohanty, R.K. | Setia, NikitaApplied Mathematics and Computation, Vol. 219 (2012), Iss. 5 P.2680
https://doi.org/10.1016/j.amc.2012.08.100 [Citations: 4]