# Fuzzy multiquadric radial basis functions for solving fuzzy partial differential equations

• M. Dirbaz
• T. Allahviranloo
Article

## Abstract

In this paper, first we define the fuzzy multiquadric radial basis functions (FMQRBF). In the following, using the (FMQRBF) as the basis functions on the fuzzy interpolation expansion, we introduce the fuzzy multiquadric radial basis functions interpolation. Moreover, by considering (FMQRBF) and our obtained fuzzy method based on generalized Hukuhara difference (modified Euler’s) (Dirbaz and Allahviranloo in Fuzzy Sets Syst 2016:1–24, 2016), we present an algorithm of the fuzzy meshless method of lines for solving fuzzy partial differential equations. Finally, by the proposed fuzzy method we solve some numerical examples and analyze the errors in details.

## Keywords

Fuzzy multi quadric radial basic functions Fuzzy interpolation Fuzzy modified Euler’s method Fuzzy partial differential equation

35A08 35A35

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## Authors and Affiliations

• M. Dirbaz
• 1
• T. Allahviranloo
• 1
• 2
1. 1.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran
2. 2.Faculty of Engineering and Natural SciencesBahcesehir UniversityIstanbulTurkey