Preprint Article Version 1 This version is not peer-reviewed

Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry

Version 1 : Received: 17 December 2017 / Approved: 18 December 2017 / Online: 18 December 2017 (10:23:51 CET)

How to cite: Mondal, S.P.; Roy, S..; Das, B..; Mahata, A.. Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry. Preprints 2017, 2017120119 (doi: 10.20944/preprints201712.0119.v1). Mondal, S.P.; Roy, S..; Das, B..; Mahata, A.. Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry. Preprints 2017, 2017120119 (doi: 10.20944/preprints201712.0119.v1).

Abstract

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

Subject Areas

fuzzy sets; fuzzy differential equation; modified runge kutta method and runge kutta mersion method

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