• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: 14, Pages: 1402-1408

Original Article

Numerical Solution of Hybrid Fuzzy Differential Equation by using Third Order Runge-Kutta Method Based on Linear Combination of Arithmetic Mean, Root Mean Square and Centroidal Mean

Received Date:09 January 2024, Accepted Date:08 March 2024, Published Date:30 March 2024


Objectives: This article develops the third order Runge-Kutta method, which uses a linear combination of the arithmetic mean, root mean square, and centroidal mean, to solve hybrid fuzzy differential equations. Methods: Seikkala's derivative is taken into account, and a numerical example is provided to show the efficacy of the proposed method. The outcomes demonstrate that the suggested approach is an effective tool for approximating the solution of hybrid fuzzy differential equations. Findings: The comparative analysis was carried out using the third order Runge-Kutta method that is currently in use and is based on arithmetic mean, root mean square, and centroidal mean. Compared to other methods, the suggested method offers a more accurate approximation. Novelty: In this study a new formula has been developed by combining three means Arithmetic Mean, Root Mean Square, and Centroidal Mean using Khattri's formula. And the developed formula is used to solve the third order Runge-Kutta method for the first order hybrid fuzzy differential equation. All real life problems which can be modeled in to an initial value problem can be solved using this formula.

Keywords: Hybrid fuzzy differential equations, Triangular fuzzy number, Seikkala's derivative, third order Runge-Kutta method, Arithmetic mean, Root mean square, Centroidal mean, Initial value problem


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© 2024 Rajakumari & Sharmila. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


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