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Title: Runge–Kutta method for solving fuzzy differential equations under generalized differentiability

Abstract

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. The Runge–Kutta approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method applicability is illustrated by solving a linear first-order fuzzy differential equation.

Authors:
 [1];  [2]
  1. Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Department of Mathematics (India)
  2. Sri Venkateswara College of Engineering (Autonomous), Department of Applied Mathematics (India)
Publication Date:
OSTI Identifier:
22769349
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; CONVERGENCE; DIFFERENTIAL EQUATIONS; ERRORS; FUZZY LOGIC; MATHEMATICAL SOLUTIONS

Citation Formats

Kanagarajan, K., E-mail: Kanagarajank@gmail.com, and Suresh, R., E-mail: sureshsiththan@gmail.com. Runge–Kutta method for solving fuzzy differential equations under generalized differentiability. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0397-6.
Kanagarajan, K., E-mail: Kanagarajank@gmail.com, & Suresh, R., E-mail: sureshsiththan@gmail.com. Runge–Kutta method for solving fuzzy differential equations under generalized differentiability. United States. doi:10.1007/S40314-016-0397-6.
Kanagarajan, K., E-mail: Kanagarajank@gmail.com, and Suresh, R., E-mail: sureshsiththan@gmail.com. Tue . "Runge–Kutta method for solving fuzzy differential equations under generalized differentiability". United States. doi:10.1007/S40314-016-0397-6.
@article{osti_22769349,
title = {Runge–Kutta method for solving fuzzy differential equations under generalized differentiability},
author = {Kanagarajan, K., E-mail: Kanagarajank@gmail.com and Suresh, R., E-mail: sureshsiththan@gmail.com},
abstractNote = {In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. The Runge–Kutta approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method applicability is illustrated by solving a linear first-order fuzzy differential equation.},
doi = {10.1007/S40314-016-0397-6},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}