CONVERGENCE AND STABILITY OF THE IMPROVED PREDICTOR CORRECTOR METHOD FOR SOLVING FUZZY DIFFERENTIAL EQUATIONS DRIVEN BY LIU'S PROCESS

S. Mansouri, M. Gachpazan, O. Fard

IJPAM: Volume 113, No. 5 (2017)

Title

CONVERGENCE AND STABILITY OF THE IMPROVED
PREDICTOR CORRECTOR METHOD FOR SOLVING
FUZZY DIFFERENTIAL EQUATIONS DRIVEN
BY LIU'S PROCESS

Authors

S. Mansouri

, M. Gachpazan

, O. Fard

$^{1,2,3}$ Department Of Applied Mathematics
School of Mathematical Sciences
Ferdowsi University Of Mashhad
Mashhad, IRAN

Abstract

Fuzzy differential equation (FDE) is a type of differential equation driven by Liu's process. In this paper, a concept of $\alpha$ -path to FDE is presented, which is a type of certain function that solves an associate ordinary differential equation. Then, an improved predictor corrector (IPC) method is introduced to solve FDEs, which essentially solves each $\alpha$ -path and produces an inverse credibility distribution of the solution. Moreover, the convergence and stability of the IPC method is presented in details. We explain that our estimation has a good degree of accuracy.

History

Received: December 11, 2016
Revised: February 2, 2017
Published: April 1, 2017

AMS Classification, Key Words

AMS Subject Classification: Key Words and Phrases: Fuzzy Liu's process, Improved predictor corrector (IPC) method, Convergence, Stability

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How to Cite?

DOI: 10.12732/ijpam.v113i5.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 5
Pages: 627 - 641

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