## Abstract

We derive a family of fourth-order finite difference schemes on the rotated grid for the two-dimensional convection-diffusion equation with variable coefficients. In the case of constant convection coefficients, we present an analytic bound on the spectral radius of the line Jacobi's iteration matrix in terms of the cell Reynolds numbers. Our analysis and numerical experiments show that the proposed schemes are stable and produce highly accurate solutions. Classical iterative methods with these schemes are convergent with large values of the convection coefficients. We also compare the fourth-order schemes with the nine point scheme obtained from the second-order central difference scheme after one step of cyclic reduction.

Original language | English |
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Pages (from-to) | 413-429 |

Number of pages | 17 |

Journal | Mathematics and Computers in Simulation |

Volume | 59 |

Issue number | 5 |

DOIs | |

State | Published - Jun 15 2002 |

### Bibliographical note

Funding Information:The research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532, and in part by NASA under grant no. NAGS-3508.

### Funding

The research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532, and in part by NASA under grant no. NAGS-3508.

Funders | Funder number |
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National Science Foundation (NSF) | CCR-0092532, CCR-9902022, CCR-9988165 |

National Aeronautics and Space Administration | NAGS-3508 |

## Keywords

- Convection-diffusion equation
- Fourth-order difference schemes
- Rotated grid

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics