Fuzzy multiquadric radial basis functions for solving fuzzy partial differential equations

被引：4

作者：

Dirbaz, M. ^{[1
]}

Allahviranloo, T. ^{[1
,2
]}

机构：

[1] Islamic Azad Univ, Dept Math, Sci & Res Branch, Tehran, Iran

[2] Bahcesehir Univ, Fac Engn & Nat Sci, Istanbul, Turkey

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2019年 / 38卷 / 04期

关键词：

Fuzzy multi quadric radial basic functions; Fuzzy interpolation; Fuzzy modified Euler's method; Fuzzy partial differential equation; APPROXIMATIONS;

D O I：

10.1007/s40314-019-0942-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：19

共 50 条

[21] The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
Piret, Cecile
JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (14) : 4662 - 4675
[22] Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients
Li, Ming
Chen, C. S.
Tsai, C. H.
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, 2010, 57 (05) : 333 - 347
[23] Gaussian-Radial Basis Functions for Solving Fractional Parabolic Partial Integro-Differential Equations
Maybodi, F. S. Aghaei
Heydari, M. H.
Ghaini, F. M. Maalek
JOURNAL OF MATHEMATICAL EXTENSION, 2021, 15 (02)
[24] Solving differential equations with radial basis functions: multilevel methods and smoothing
Fasshauer, GE
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1999, 11 (2-3) : 139 - 159
[25] Solving differential equations with radial basis functions: multilevel methods and smoothing
Gregory E. Fasshauer
Advances in Computational Mathematics, 1999, 11 : 139 - 159
[26] Fuzzy partial differential equations
Abualhomos, Mayada
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (02): : 301 - 306
[27] Usage of the Fuzzy Adomian Decomposition Method for Solving Some Fuzzy Fractional Partial Differential Equations
Saeed, Nagwa A.
Pachpatte, Deepak B.
ADVANCES IN FUZZY SYSTEMS, 2024, 2024
[28] Solving Partial Fuzzy Integro-Differential Equations Using Fuzzy Sumudu Transform Method
Georgieva, Atanaska
Spasova, Mira
SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020), 2021, 2321
[29] On the effect of order of radial basis functions in the solution of partial differential equations
Hutchcraft, W. Elliott
Gordon, Richard K.
2007 IEEE ANTENNAS AND PROPAGATION SOCIETY INTERNATIONAL SYMPOSIUM, VOLS 1-12, 2007, : 3317 - 3320
[30] Solve partial differential equations by two or more radial basis functions
Zhang, Yunxin
APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (01) : 793 - 801

← 1 2 3 4 5 →