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**A modified decomposition.**
*(English)*
Zbl 0756.35013

Summary: The Maclaurin series is quite limited in comparison to the (Adomian) series obtained in the decomposition method. By adding procedures from the decomposition method and the expansion of nonlinearities using the Adomian polynomials, as well as a recent result of the first two authors [Appl. Math. Lett. 4, No. 4, 69-71 (1991; Zbl 0742.40004)] on transformation of series using the above polynomials, the Maclaurin series can be made much more useful in its applicability. However, the convergence is still slower than for the second author’s earlier results using decomposition [Comput. Math. Appl. 21, No. 5, 101-127 (1991; Zbl 0732.35003)].

### MSC:

35C10 | Series solutions to PDEs |

65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

65N99 | Numerical methods for partial differential equations, boundary value problems |

65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |

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\textit{R. Rach} et al., Comput. Math. Appl. 23, No. 1, 17--23 (1992; Zbl 0756.35013)

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### References:

[1] | Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Int. J. Comp. and Math. with Applic., 21, 5, 101-128 (1991) · Zbl 0732.35003 |

[2] | Adomian, G., On solution of complex dynamical systems, Part I and Part II, Simulation, 54, 5, 245-251 (1990) |

[3] | Adomian, G., Decomposition solution of nonlinear hyperbolic equations, (Seventh Int. Conf. on Math. and Computer Modelling. Seventh Int. Conf. on Math. and Computer Modelling, Chicago (Aug. 4, 1989)), Presented at the · Zbl 0729.65072 |

[4] | Adomian, G.; Rach, R., Multiple decompositions for computational convenience, Appl. Math. Ltrs., 3, 3, 97-99 (1990) · Zbl 0707.34008 |

[5] | Adomian, G.; Rach, R., Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations, Int. J. Comput. and Math. with Applic., 19, 12, 9-12 (1990) · Zbl 0702.35058 |

[7] | Adomian, G.; Rach, R., Transformations of series, Appl. Math. Ltrs., 4, 4, 69-72 (1991) · Zbl 0742.40004 |

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