A Numerical Algorithm for Solving Impulsive Fuzzy Initial Value Problem Based on Fuzzy Methods
Subject Areas : International Journal of Industrial Mathematicsمحدثه دیرباز 1 , سعید عباسبندی 2
1 - Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Imam Khomeini International University, Qazvin, Iran.
Keywords: Multline, Fuzzy Modified Euler's method, Generated of Hukuhara difference, Impulsive fuzzy differential equation,
Abstract :
In this paper, first the Newton’s divided difference interpolation method based on the gH difference on fuzzy data is introduced. Then the numerical methods entitled fuzzy Euler and modified fuzzy Euler are used to solve fuzzy impulsive initial value problem. Moreover the algorithms for the fuzzy impulsive initial value problem are explained and their local truncation errors are obtained in details. Finally, for more illustration some numerical examples are solved.
[1] T. Akther, S. U. Ahmad, A Computational Method For Fuzzy Arithmetic Operations, Daffodil International University journal of science and technology 11 (2009) 19-20.
[2] T. Allahviranloo, Z. Gouyandeh, A. Armand, A Method for Solving Fuzzy Differential Equation Based on Fuzzy Taylor Expansion, IOS press 32 (2015) 1-16.
[3] B. Bede, L. Stefanini, Generalized differentiability of fuzzy valued functions, Fuzzy Sets and Systems 230 (2013) 119-141.
[4] M. Benchohra, J. Henderson, S. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, (2006).
[5] M. Benchohra, JUAN J. Nieto, A. Ouahab, Fuzzy solution for impulsive differential equations, Applied Analysis 11 (2007) 379-394.
[6] P. Phani Bushan Rao, N. Ravi Shankar, Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality, Advances in Fuzzy Systems, (2011).
[7] B. M. Randelovic, L. V. Stefanovic, B. M. Dankovic, Numerical solution of impulsive differential equations, Facta Univ. Ser Math. Inform 15 (2000) 101-111.
[8] N. Shamsiah Amir Hamzah, Mustafa Mamat, J. Kavikumar, S. W. Lee, Noor’ani Ahmad, Impulsive Differential Equations by Using the Euler Method, Appl. Mathematical Sci 4 (2010) 3219-3232.
[9] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987) 319-330.
[10] J. Shokri, Numerical solution of fuzzy differential equations, Applied Mathematical Sciences 1 (2007) 2231-2246.
[11] A. M. Samailenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.