Numerical Investigation of the Hybrid Fuzzy Differential Equations Using Leapfrog Method

Abstract

In this paper, We develop the Leapfrog method for solving hybrid fuzzy differential equations (HFDE) based on the generalized concept of higherorder fuzzy differentiability [19]. The obtain discrete solutions were compared with another method taken from the literature [19]. The new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. The numerical example was given to illustrate the efficiency of the method.

Numerical investigation of the fuzzy integro-differential equations by He$’$s Homotopy perturbation method

“…If we take He's homotopy perturbation method [14][15][16][17][18][19][20][21] getting applied to the wide class problems in physics, biology and chemical reactions. If provides this result in a computable terms of rapid convergent series.…”

“…Recently Abbasbandy [1] found the solution of Kawahara equation, generalized Zakharov equation [S. Abbasbandy, E. Babolian and M. Ashtiani [4]], MHD Falkne-Skan flow [S. Abbasbandy and T. Hayat [5]] and nonlinear boundary value problems [S. Abbasbandy and E. Shivanian [6]]. In this article we developed numerical methods for FIDE to get the discrete solutions via He's Homotopy Perturbation method which was studied by Sekar et al [14][15][16][17][18][19][20][21]. The problems are solved in two methods; one is single-term Haar wavelet series method (STHWS) which is presented previously by Sekar et al [13] and another one is He's Homotopy Perturbation method which has been developed exclusively to deal with fuzzy integrodifferential equations.…”

Numerical investigation of the hybrid fuzzy differential equations using He's homotopy perturbation method

“…Recently, T.Jayakumar and K. Kanagarajan [3] solved the hybrid fuzzy differential equations using Adams Fifth Order Predictor-Corrector Method. S. Sekar and K. Prabhavathi [13] solved the same hybrid fuzzy differential equations using Leapfrog method. The objective of this paper is to use the He's Homotopy Perturbation Method (discussed by Sekar et al [14][15][16]) to solve the hybrid fuzzy differential equations (discussed by T.Jayakumar and K. Kanagarajan [3] and S. Sekar and K. PRabhavathi [13]).…”

“…The proposed method is tested on hybrid fuzzy differential equations. The discrete solutions obtained through He's Homotopy Perturbation Method are compared with Leapfrog method [13]. The applicability of the He's Homotopy Perturbation Method is more suitable to solve the hybrid fuzzy differential equations.…”

A Study on unsteady one-dimensional heat flow problem using Rayleigh Ritz, Single-term Walsh series and Leapfrog Method

“…In this paper we developed numerical methods for addressing unsteady one-dimensional heat-flow problem by an application of the Leapfrog method which was studied by Sekar and team of his researchers [1][2][6][7][8][9][10][11][12][13][14][15][16][17][18], which involve two phases. In phase-I, the spatial dependency of the heat flow equation is eliminated by applying the Rayleigh-Ritz method and to determine the suitable initial conditions, the Galerkin Technique is utilized.…”