Fuzzy differential equations and applications for engineers and scientists /
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 defi...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
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Boca Raton, FL :
CRC Press, Taylor & Francis Group,
[2017]
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of 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.