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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Snehashish Chakraverty; Smita Tapaswini; D Behera |

ISBN: | 9781482244762 1482244764 9781315372853 1315372851 |

OCLC Number: | 960716609 |

Target Audience: | College Audience |

Description: | 1 online resource |

Contents: | Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Acknowledgements; Authors; Chapter 1: Preliminaries of Fuzzy Set Theory; Bibliography; Chapter 2: Basic Concepts of Fuzzy and Fuzzy Fractional Differential Equations; 2.1 n-th Order Fuzzy Differential Equations; 2.2 Fractional Initial Value Problem; 2.3 Fuzzy Fractional Initial Value Problem; Bibliography; Chapter 3: Analytical Methods of Fuzzy Differential Equations; 3.1 Recent Proposed Methods; 3.1.1 Method 1: Fuzzy Centre-Based Method; 3.1.2 Method 2: Method Based on Addition and Subtraction of Fuzzy Numbers. 3.1.3 Method 3: Fuzzy Centre and Fuzzy Radius-Based Method3.1.4 Method 4: Double Parametric-Based Method; Bibliography; Chapter 4: Numerical Methods for Fuzzy Ordinary and Partial Differential Equations; 4.1 Euler-Type Methods; 4.1.1 Method 1: Max-Min Euler Method; 4.1.2 Method 2: Average Euler Method; 4.2 Improved Euler-Type Methods; 4.2.1 Method 3: Max-Min Improved Euler Method; 4.2.2 Method 4: Average Improved Euler Method; 4.3 Weighted Residual Methods; 4.3.1 Method 5: Collocation-Type Method; 4.3.2 Method 6: Galerkin-Type Method; 4.4 The Homotopy Perturbation Method. 4.5 The Adomian Decomposition Method4.6 The Variational Iteration Method; Bibliography; Chapter 5: Application of Numerical Methods to Fuzzy Ordinary Differential Equations; 5.1 Implementation of Methods 1 and 2; 5.2 Implementation of Methods 3 and 4; 5.3 Implementation of Method 5; 5.4 Implementation of Method 6; 5.5 Implementation of the Homotopy Perturbation Method; Bibliography; Chapter 6: Fuzzy Structural Problems; 6.1 Double Parametric-Based Solution of an Uncertain Beam; 6.2 Solution of Uncertain Beam; 6.2.1 Using HPM; 6.2.2 Using ADM; 6.3 Uncertain Response Analysis; 6.3.1 Using HPM. 6.3.2 Using ADM6.4 Numerical Results; Bibliography; Chapter 7: Fuzzy Vibration Equations of Large Membranes; 7.1 Double Parametric-Based Solution of Uncertain Vibration Equations of Large Membranes; 7.2 Solutions of Fuzzy Vibration Equations of Large Membranes; 7.2.1 Solution by HPM; 7.2.2 Solution by ADM; 7.3 Solution Bounds for Particular Cases; 7.3.1 Using HPM; 7.3.2 Using ADM; 7.4 Numerical Results; Bibliography; Chapter 8: Nonprobabilistic Uncertainty Analysis of the Forest Fire Model; 8.1 Modelling of Forest Fire; 8.2 Fuzzy Solution of Fire Propagation; 8.3 Numerical Results. |

Responsibility: | S. Chakraverty, Smita Tapaswini, Diptiranjan Behera. |

### Abstract:

Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique workprovides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.

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