Homotopy Analysis Method Analytical Scheme for Developing a Solution to Partial Differential Equations in Fuzzy Environment

被引：14

作者：

Altaie, Sarmad A. ^{[1
]}

Anakira, Nidal ^{[2
]}

Jameel, Ali ^{[3
]}

Ababneh, Osama ^{[4
]}

Qazza, Ahmad ^{[4
]}

Alomari, Abdel Kareem ^{[5
]}

机构：

[1] Univ Technol Iraq, Comp Engn Dept, Baghdad 10066, Iraq

[2] Irbid Natl Univ, Fac Sci & Technol, Dept Math, Irbid 21110, Jordan

[3] Univ Utara Malaysia UUM, Sch Quantitat Sci SQS, Inst Strateg Ind Decis Modelling ISIDM, Sintok 06010, Kedah, Malaysia

[4] Zarqa Univ, Fac Sci, Dept Math, Zarqa 13110, Jordan

[5] Yarmouk Univ, Fac Sci, Dept Math, Irbid 21163, Jordan

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 08期

关键词：

fuzzy partial differential equations; fuzzy wave equation; fuzzy reaction-diffusion equation; fuzzy set theory; approximate analytical solution; homotopy analysis method; APPROXIMATE SOLUTION TECHNIQUE; SMALL PARAMETERS; MODEL;

D O I：

10.3390/fractalfract6080419

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Partial differential equations are known to be increasingly important in today's research, and their solutions are paramount for tackling numerous real-life applications. This article extended the analytical scheme of the homotopy analysis method (HAM) to develop an approximate analytical solution for Fuzzy Partial Differential Equations (FPDEs). The scheme used its powerful tools, the auxiliary function and convergence-control parameter, in the analysis and optimization, which ensures the convergence of the approximate series solution in addition to considering all necessary concepts from fuzzy set theory to provide high precision in the fuzzy environment. Furthermore, the efficiency was shown by applying the proposed scheme to linear and nonlinear cases of Fuzzy Reaction-Diffusion Equation (FRDE) and Fuzzy Wave Equation (FWE).

引用

页数：22

共 48 条

[1] Differential calculus of fuzzy multi-variable functions and its applications to fuzzy partial differential equations [J].

Alikhani, R. ;

Bahrami, F. ;

Parvizi, S. .

FUZZY SETS AND SYSTEMS, 2019, 375 :100-120

[2] Fuzzy partial differential equations under the cross product of fuzzy numbers [J].

Alikhani, R. ;

Bahrami, F. .

INFORMATION SCIENCES, 2019, 494 :80-99

[3] The exact solutions of fuzzy wave-like equations with variable coefficients by a variational iteration method [J].

Allahviranloo, T. ;

Abbasbandy, S. ;

Rouhparvar, H. .

APPLIED SOFT COMPUTING, 2011, 11 (02) :2186-2192

[4] A new method for solving fuzzy linear differential equations [J].

Allahviranloo, T. ;

Abbasbandy, S. ;

Salahshour, S. ;

Hakimzadeh, A. .

COMPUTING, 2011, 92 (02) :181-197

[5]

Allahviranloo T., 2002, Computational Methods in Applied Mathematics, V2, DOI 10.2478/cmam-2002-0014

[6] A fuzzy solution of wave equation by FFS-transform [J].

Allahviranloo, Tofigh ;

Ghobadi, Mostafa ;

Matinfar, Mashallah .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2024, 40 (01)

[7] On fuzzy solutions for heat equation based on generalized Hukuhara differentiability [J].

Allahviranloo, Tofigh ;

Gouyandeh, Zienab ;

Armand, Atefeh ;

Hasanoglu, Alemdar .

FUZZY SETS AND SYSTEMS, 2015, 265 :1-23

[8]

Altaie SA, 2021, INT J COMPUT SCI MAT, V13, P136

[9] Series Solution of Fuzzy Linear Cauchy Reaction-Diffusion Equation by Using Homotopy Perturbation Method [J].

Altaie, Sarmad A. ;

Saaban, Azizan ;

Jameel, Ali F. .

13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017), 2017, 1905

[10]

[Anonymous], 2004, Introduction to the Homotopy Analysis Method

← 1 2 3 4 5 →