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

[31] AN APPROXIMATE SOLUTION TECHNIQUE NOT DEPENDING ON SMALL PARAMETERS - A SPECIAL EXAMPLE [J].

LIAO, SJ .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1995, 30 (03) :371-380

[32] A kind of approximate solution technique which does not depend upon small parameters .2. An application in fluid mechanics [J].

Liao, SJ .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1997, 32 (05) :815-822

[33] Solving fuzzy partial differential equations by fuzzy two-dimensional differential transform method [J].

Mikaeilvand, N. ;

Khakrangin, S. .

NEURAL COMPUTING & APPLICATIONS, 2012, 21 :S307-S312

[34] A novel computing three-dimensional differential transform method for solving fuzzy partial differential equations [J].

Mirzaee, Farshid ;

Yari, Mohammad Komak .

AIN SHAMS ENGINEERING JOURNAL, 2016, 7 (02) :695-708

[35]

Mondal S.P., 2013, Journal of Soft Computing and Applications, P1, DOI [10.5899/2013/jsca-00032, DOI 10.5899/2013/JSCA-00032]

[36] Fuzzy parameters in a partial differential equation model for population dispersal of leaf-cutting ants [J].

Motta Jafelice, R. ;

Almeida, C. ;

Meyer, J. F. C. A. ;

Vasconcelos, H. L. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (06) :3397-3412

[37]

Nemati K., 2008, J. Nonlinear Sci. Appl, V1, P61, DOI [DOI 10.22436/JNSA.001.02.02, 10.22436/jnsa.001.02.02]

[38]

Olver P.J., 2014, Introduction to partial differential equations, P635

[39]

Osman M., 2021, Open J. Math. Anal, V5, P51, DOI DOI 10.30538/PSRP-OMA2021.0082

[40] Comparison of fuzzy Adomian decomposition method with fuzzy VIM for solving fuzzy heat-like and wave-like equations with variable coefficients [J].

Osman, Mawia ;

Gong, Zengtai ;

Mustafa, Altyeb Mohammed .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

← 1 2 3 4 5 →