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

Abstract

In this paper, the authors introduced the He's Homotopy Perturbation Method (HHPM) for solving the Fuzzy Integro-Differential equations (FIDE) [13]. The obtain discrete solutions were compared with another method taken from the literature [13]. The new method has a lower computational cost which effects the time consumption. The numerical example was given to highlight the efficiency of this method.

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

“…In this section, we briefly review the main points of the powerful method, known as the He's homotopy perturbation method [14][15][16]. To illustrate the basic ideas of this method, we consider the following differential equation:…”

“…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]).…”

Numerical investigation of the nonlinear integro-differential equations using He's homotopy perturbation method

“…In this article we developed numerical methods for nonlinear IDEs to get discrete solutions via He's Homotopy Perturbation method which was studied by S. Sekar et al [3,4]. The subject of this paper is to try to find numerical solutions of nonlinear integro-differential equations using He's Homotopy Perturbation method and compare the discrete results with the single-term Haar wavelet series method (STHWS) which is presented previously by Sekar et al [2].…”

On solution of fuzzy Volterra integro-differential equations

“…Many scholars have contributed, to investigate and studying solutions of FIDEs and FIEs utilizing different numerical and analytical techniques. These techniques include the iterative approximation technique (Abigail, 2019), He's homotopy perturbation method (Sekar & Thirumurugan, 2019), Laplace Adomian Decomposition method (Bushnaq, Ullah, Ullah, & Shah, 2020;Ullah, Ullah, Abdeljawad, Hammouch, & Shah, 2021;Ullah, Ullah, Shah, & Baleanu, 2020), Sumudu decomposition method (Kang, Iqbal, Habib, & Nazeer, 2019), fuzzy differential transform method (Biswas & Roy, 2018), and Kernel Hilbert space method (Gumah, Naser, Al-Smadi, & Al-Omari, 2018), and others (Hooshangian, 2019). The scholars also investigated the existence and the uniqueness of the solution for FIDEs and FIEs (Ali, 2018;Georgieva, 2020;Sindu Devi & Ganesan, 2018;Tunc¸& Tunc¸, 2018).…”