Numerical Accuracy of the Predictor-Corrector Method to Solve Fuzzy Differential Equations Based on the Stochastic Arithmetic

Abstract

In this work, a reliable scheme is proposed to solve fuzzy differential equation based on the predictor-corrector methods (PC-methods) under generalized H-differentiability. For this purpose, the stochastic arithmetic(SA) and the CESTAC* method are applied to validate the results. Also, the numerical accuracy of the method is proved and an algorithm is given based on the new arithmetic. In order to implement C++ codes, the CADNA† library is used. In this case, the optimal number of nodes and optimal step size are found. The examples illustrate the efficiency and importance of using the SA in place of the floating-point arithmetic(FPA).

Keywords:

• Fuzzy differential equation(FDE)
• Predictor-Corrector method
• multi-step method
• stochastic arithmetic
• CESTAC method
• CADNA library

Acknowledgments

The authors would like to thank the anonymous referees for their constructive comments to improve the quality of this work.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mohammad Ali Fariborzi Araghi

Mohammad Ali Fariborzi Araghi was born in Tehran, Iran. He received B.SC. degree in mathematics from Kharazmi university, M.SC. degree in applied mathematics from Islamic Azad university, Karaj branch and Ph.D. degree in applied mathematics, numerical analysis field, from Islamic Azad university, Science and Research branch. He is the associate professor of Islamic Azad university, Central Tehran branch. His research interests are numerical solutions of integral or differential equations and applications of fuzzy mathematics.

Hasan Barzegar Kelishami

Hasan Barzegar Kelishami was born in Gilan, Iran. He received B.SC. degree in mathematics from Islamic Azad university, Karaj branch, M.SC. degree in applied mathematics from Islamic Azad university, Science and Research branch and Ph.D. degree in applied mathematics, numerical analysis field, from Islamic Azad university, Central Tehran branch. He is a lecturer of Islamic Azad university, North Tehran branch, now. His research interests are numerical solutions of integral or differential equations and applications of fuzzy mathematics.