### Abstract

This paper uses the sinc methods to construct a solution of the Laplace's equation using two solutions of the heat equation. A numerical approximation is obtained with an exponential accuracy. We also present a reliable algorithm of Adomian decomposition method to construct a numerical solution of the Laplace's equation in the form a rapidly convergence series and not at grid points. Numerical examples are given and comparisons are made to the sinc solution with the Adomian decomposition method. The comparison shows that the Adomian decomposition method is efficient and easy to use.

Original language | English |
---|---|

Pages (from-to) | 1271-1283 |

Number of pages | 13 |

Journal | Applied Mathematics and Computation |

Volume | 170 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 15 2005 |

### Fingerprint

### Keywords

- Adomian decomposition method
- Laplace equation
- Numerical experiments
- Sinc function

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

*Applied Mathematics and Computation*,

*170*(2), 1271-1283. https://doi.org/10.1016/j.amc.2005.01.018

**Numerical solutions of the Laplace's equation.** / Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 170, no. 2, pp. 1271-1283. https://doi.org/10.1016/j.amc.2005.01.018

}

TY - JOUR

T1 - Numerical solutions of the Laplace's equation

AU - Al-Khaled, Kamel

PY - 2005/11/15

Y1 - 2005/11/15

N2 - This paper uses the sinc methods to construct a solution of the Laplace's equation using two solutions of the heat equation. A numerical approximation is obtained with an exponential accuracy. We also present a reliable algorithm of Adomian decomposition method to construct a numerical solution of the Laplace's equation in the form a rapidly convergence series and not at grid points. Numerical examples are given and comparisons are made to the sinc solution with the Adomian decomposition method. The comparison shows that the Adomian decomposition method is efficient and easy to use.

AB - This paper uses the sinc methods to construct a solution of the Laplace's equation using two solutions of the heat equation. A numerical approximation is obtained with an exponential accuracy. We also present a reliable algorithm of Adomian decomposition method to construct a numerical solution of the Laplace's equation in the form a rapidly convergence series and not at grid points. Numerical examples are given and comparisons are made to the sinc solution with the Adomian decomposition method. The comparison shows that the Adomian decomposition method is efficient and easy to use.

KW - Adomian decomposition method

KW - Laplace equation

KW - Numerical experiments

KW - Sinc function

UR - http://www.scopus.com/inward/record.url?scp=27144440503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27144440503&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2005.01.018

DO - 10.1016/j.amc.2005.01.018

M3 - Article

VL - 170

SP - 1271

EP - 1283

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2

ER -