### 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 |
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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 |

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

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## Cite this

Al-Khaled, K. (2005). Numerical solutions of the Laplace's equation.

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