# 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:

- Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Department of Mathematics (India)
- 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}

}

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