Solving Fuzzy Ordinary Differential Equations Using Homotopy Analysis Method
DOI:
https://doi.org/10.54172/bjhz9304Keywords:
Fuzzy Concepts, Fuzzy Ordinary Equations, Homotopy Analysis MethodAbstract
Fuzzy ordinary differential equations (FODEs) extend classical ordinary differential equations (ODEs) to systems characterized by uncertainty and imprecision, often modeled using fuzzy set theory. In this work we use homotopy analysis method (HAM) to solve FODEs, and show how HAM works. (HAM) is an easy and effective method to solve linear and nonlinear ordinary differential equations. HAM does not need small parameters or special tricks like linearization. Instead, it builds a smooth path from a simple starting guess to the real solution by using a special parameter and function.
References
Ali R. H. and Ibraheem K. I (2020) Solution of Fuzzy Initial Value Problems Using Homotopy Analysis Method and Padè Approximate. Open Access Library Journal, 7: 1-16.
Ghanbari M. (2012) Solution of the first order linear fuzzy differential equations by some reliable methods, Journal of fuzzy set valued analysis.
Gong Z and Shao Y. (2008) Global Existence and Uniqueness of Solution for Fuzzy Differential Equations Under Dissipative-Tape Conditions. Journal of Computers and Mathematics with Applications, 56 2716-2723.
Gasilov N. A., Hashimoglu S. E. and et al. (2012) A New Approach to Non-Homogeneous Fuzzy Initial Value Problem. Computer Modeling in Engineering & Sciences, 85(4):367-378.
Jameel A., (2015) Approximate Solution of First Order Nonlinear Fuzzy Initial Value Problem with Two Different Fuzzifications. Journal of uncertain systems 9(3):221-229.
Jameel A., Ghoriishi M. and et all. (2014) Approximate Solution of High Order Fuzzy Initial Value Problems. Journal of Uncertain Systems, 8(2) 149-160.
Liao S. (2011) Homotopy analysis Method in Non-Linear Differential Equations. Springer, Shanghai, China.
Nadeem M., Jamshad A., Fatima N., Loredana F. I. (2023). Fuzzy Solutions of some variants of the fractional order Korteweg-de-Vries equations via an analytical method Alexandria Engineering Journal 80 8–21.
Shokri J, (2007), Numerical Solution of Fuzzy Differential Equations. Journal of Applied Mathematical Sciences, 1(45) 2231-2246.
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