### 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 |
---|---|

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 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics

### Cite this

*Applied Mathematics and Computation*,

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

**A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws.** / Az-Zo'Bi, Emad A.; Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 217, no. 8, pp. 4248-4256. https://doi.org/10.1016/j.amc.2010.10.040

}

TY - JOUR

T1 - A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws

AU - Az-Zo'Bi, Emad A.

AU - Al-Khaled, Kamel

PY - 2010/12/15

Y1 - 2010/12/15

N2 - 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.

AB - 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.

KW - Adomian polynomials

KW - Cauchy problem

KW - Conservation law

KW - Decomposition method

KW - Hyperbolic-elliptic system

UR - http://www.scopus.com/inward/record.url?scp=78649926129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649926129&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2010.10.040

DO - 10.1016/j.amc.2010.10.040

M3 - Article

VL - 217

SP - 4248

EP - 4256

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 8

ER -