### Abstract

In this paper, we propose a new convergence proof of the Adomian's decomposition method (ADM), applied to the generalized nonlinear system of partial differential equations (PDE's) based on new formula for Adomian polynomials. The decomposition scheme obtained from the ADM yields an analytical solution in the form of a rapidly convergent series for a system of conservation laws. Systems of conservation laws is presented, we obtain the stability of the approximate solution when the system changes type. We show with an explicit example that the latter property is true for general Cauchy problem satisfying convergence hypothesis. The results indicate that the ADM is effective and promising.

Original language | English |
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Pages (from-to) | 4248-4256 |

Number of pages | 9 |

Journal | Applied Mathematics and Computation |

Volume | 217 |

Issue number | 8 |

DOIs | |

Publication status | Published - Dec 15 2010 |

### Keywords

- Adomian polynomials
- Cauchy problem
- Conservation law
- Decomposition method
- Hyperbolic-elliptic system

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics

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## Cite this

*Applied Mathematics and Computation*,

*217*(8), 4248-4256. https://doi.org/10.1016/j.amc.2010.10.040