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

Abstract

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