### 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 language | English |
---|---|

Pages (from-to) | 453-470 |

Number of pages | 18 |

Journal | Neural, Parallel and Scientific Computations |

Volume | 14 |

Issue number | 4 |

Publication status | Published - Dec 2006 |

### Fingerprint

### 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

*Neural, Parallel and Scientific Computations*,

*14*(4), 453-470.

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

Research output: Contribution to journal › Article

*Neural, Parallel and Scientific Computations*, vol. 14, no. 4, pp. 453-470.

}

TY - JOUR

T1 - Fourth order nine point unequal mesh discretization for the solution of 2D nonlinear elliptic partial differential equations

AU - Mohanty, R. K.

AU - Karaa, Samir

AU - Arora, Urvashi

PY - 2006/12

Y1 - 2006/12

N2 - 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.

AB - 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.

KW - Burger's equation

KW - Fourt order scheme

KW - Line iterative method

KW - Navier-Stokes equation

KW - Nonlinear elliptic equation

KW - Poisson's equation

KW - Unequal mesh size

UR - http://www.scopus.com/inward/record.url?scp=34249309930&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249309930&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34249309930

VL - 14

SP - 453

EP - 470

JO - Neural, Parallel and Scientific Computations

JF - Neural, Parallel and Scientific Computations

SN - 1061-5369

IS - 4

ER -