Fourth order nine point unequal mesh discretization for the solution of 2D nonlinear elliptic partial differential equations

R. K. Mohanty, Samir Karaa, Urvashi Arora

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We propose a nine point fourth order accurate compact difference scheme with unequal mesh size in different coordinate directions and discuss line iterative methods for the solution of elliptic partial differential equations with variable coefficients subject to appropriate Dirichlet boundary conditions. We also prove the convergence of line iterative methods for solving the linear system arising from proposed discretization of a two dimensional diffusion-convection equation. The proposed method is successfully applied to solve singular elliptic equation, model Burgers' equation and Navier Stokes equations of motion in a rectangular domain. Finally, we perform numerical experiments to demonstrate the high accuracy and stability advantages of the proposed new scheme.

Original languageEnglish
Pages (from-to)453-470
Number of pages18
JournalNeural, Parallel and Scientific Computations
Volume14
Issue number4
Publication statusPublished - Dec 2006

Fingerprint

Elliptic Partial Differential Equations
Iterative methods
Unequal
Nonlinear Partial Differential Equations
Partial differential equations
Fourth Order
Discretization
Mesh
Singular Elliptic Equation
Iteration
Compact Scheme
Line
Convection-diffusion Equation
Burgers Equation
Difference Scheme
Variable Coefficients
Dirichlet Boundary Conditions
Navier Stokes equations
Equations of motion
Linear systems

Keywords

  • Burger's equation
  • Fourt order scheme
  • Line iterative method
  • Navier-Stokes equation
  • Nonlinear elliptic equation
  • Poisson's equation
  • Unequal mesh size

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Fourth order nine point unequal mesh discretization for the solution of 2D nonlinear elliptic partial differential equations. / Mohanty, R. K.; Karaa, Samir; Arora, Urvashi.

In: Neural, Parallel and Scientific Computations, Vol. 14, No. 4, 12.2006, p. 453-470.

Research output: Contribution to journalArticle

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