NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS

Bayrak, Mine Aylin; Can, Emine

NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS

Mine Aylin BAYRAK, (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İzmit-Kocaeli, Türkiye)

Emine CAN (İstanbul Medeniyet Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Fizik Mühendisliği Bölümü, İstanbul, Türkiye)

TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics

6 1

Yıl: 2020 Cilt: 10 Sayı: 4 Sayfa Aralığı: 886 - 896 Metin Dili: İngilizce İndeks Tarihi: 03-05-2021

NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS

Öz:

Abstract.In this study, we consider the concept of under generalized differentiabilityfor the fuzzy parabolic differential equations. When the fuzzy derivative is consideredas generalization of theH-derivative, for our case, the fuzziness is in the coefficents aswell as initial and boundary conditions. We analysed and applied to numerically solvea fuzzy parabolic equation by finite difference method. The applicability of presented algorithm is illustrated by solving an examples of fuzzy partial differential equations.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Tofigh, A.,(2006), Difference methods for fuzzy partial differential equation, Comput. Methods Appl.Math.,3, pp.233-242.
[2] Tofigh, A., Gouyandeh,Z., Armand, A. and Hasanoglu, A., (2015), On fuzzy solutions for heat equationbased on generalized Hukuhara differentiability, Fuzzy Sets and Systems, 265, pp.1-23.
[3] Bede, B.,(2013), Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, London.
[4] Bede,B. and Gal,S.G.,(2005), Generalizations of the differentibility of fuzzy-number-valued functionswith applications to FDEs, Fuzzy Sets and Syst., 151, pp.581-599.
[5] Gazanfari, B. and Ebrahimi, P., (2015), Differential transformation method for solving fuzzy fractionalheat equation, Int. J. Math. Model. Comput., 5, pp.81-89.
[6] Bede,B. and Stefanini,L.,(2013), Generalized differentiability of fuzzy-valued functions, Fuzzy Sets andSyst., 230, pp.119-141.
[7] Bertone, A.M., Jafelice,R.M., Barros, L.C. and Bassanezi, R.C.,(2013), On fuzzy solutions for partialdifferential equations, Fuzzy Sets and Syst., 219, pp.68-80.
[8] Buckley, J.J. and Feuring, T., (1999),Introduction to fuzzy partial differential equations, Fuzzy Setsand Syst., 105, pp.241-248.
[9] Chalco-Cano,Y. and Roman-Flores, H.,(2008),On new solutions of FDEs, Chaos, Solitons and Fractals,38, pp.112-119.
[10] Chen, Y.Y., Chang,Y.T.and Chen, B.S.(2009), Fuzzy solutions to partial differential equations: adap-tive approach, IEEE Trans. Fuzzy Syst., 17 , pp.116-127.
[11] Diamond, P. and Kloeden, P.,(1994), Metric Spaces of Fuzzy Sets, World Scientific, Singapore.
[12] Georgiou, D.N., Nieto,J.J.and Rodriguez-Lopez, R.,(2005),Initial value problems for higher-orderfuzzy differential equations, Nonlin. Analy., 63 pp.587-600.
[13] Gouyandeh, Z., Allahviranloo, T., Abbasbandy,S. and Armand, A.,(2017),A fuzzy solution of heatequation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets and Syst.,309, pp.81-97.
[14] Kaleva, O.,(2006), A note on FDE’s, Nonlin. Anal., 64, pp.895-900.
[15] Khastan, A., Bahrami, F. and Ivaz, K.,(2009), New Results on Multiple Solutions for Nth-order FuzzyDifferential Equations under Generalized Differentiability, Boundary Value Prob., Article ID 395714.
[16] Khastan, A. and Rodriguez-Lopez,R.,(2016) On the solutions to first order linear fuzzy differentialequations, Fuzzy Sets and Syst., 295, pp.114-135.
[17] Long,H.V., Son, N.T.K. and Tam,H.T.T., (2017),The solvability of fuzzy fractional partial differentialequations under Caputo gH-differentiability, Fuzzy Sets and Syst., 309, pp.35-63.
[18] Hamzeh,Z., Izani Ismail,A. and Sathasivam,S., (2018),Numerical solution of Fuzzy fractional par-tial differential equations by an implicit finte difference scheme, Neural Comput. and Appl., DOI:10.1007/s00521-017-3299-7.
[19] Stefanini,L. and Bede,B., (2009),Generalized Hukuhara differentiability of interval-valued functionsand interval differential equations, Nonlin. Anal., 71, pp.1311-1328.
[20] Stefanini, L., (2010),A generalization of Hukuhara difference and division for interval and fuzzy arith-metic, Fuzzy Sets and Syst., 161, pp.1564-1584.
[21] Seikkala, S.,(1987), On the fuzzy initial value problem, Fuzzy Sets Syst. 24,(3), pp.319–330.
[22] Dubois , D. and Prade , H.,(1982),Towards fuzzy differential calculus part 3: differentiation, FuzzySets Syst. 8,(3), pp.225-233.
[23] Faybishenko, B.A., (2004),Introduction to modeling of hydrogeologic systems using fuzzy partial dif-ferential equation, Fuzzy Partial Diff. Eq. and Relational Eq., pp.267-284.
[24] Khastan,A. and Rodriguez-Lopez,R.,(2019), An existence and uniqueness result for fuzzy Goursatpartial differential equation, Fuzzy Sets Syst.,375 , pp.141-160.
[25] Alikhani,R., Bahrami,F. and Parvizi,S.,(2019), Differential calculus of fuzzy multi-variable functionsand its applications to fuzzy partial differential euations, Fuzzyy Syst.,375 , pp.100-120.

APA	Bayrak M, Can E (2020). NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. , 886 - 896.
Chicago	Bayrak Mine Aylin,Can Emine NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. (2020): 886 - 896.
MLA	Bayrak Mine Aylin,Can Emine NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. , 2020, ss.886 - 896.
AMA	Bayrak M,Can E NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. . 2020; 886 - 896.
Vancouver	Bayrak M,Can E NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. . 2020; 886 - 896.
IEEE	Bayrak M,Can E "NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS." , ss.886 - 896, 2020.
ISNAD	Bayrak, Mine Aylin - Can, Emine. "NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS". (2020), 886-896.

APA	Bayrak M, Can E (2020). NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 10(4), 886 - 896.
Chicago	Bayrak Mine Aylin,Can Emine NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 10, no.4 (2020): 886 - 896.
MLA	Bayrak Mine Aylin,Can Emine NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, vol.10, no.4, 2020, ss.886 - 896.
AMA	Bayrak M,Can E NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2020; 10(4): 886 - 896.
Vancouver	Bayrak M,Can E NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2020; 10(4): 886 - 896.
IEEE	Bayrak M,Can E "NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS." TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 10, ss.886 - 896, 2020.
ISNAD	Bayrak, Mine Aylin - Can, Emine. "NUMERICAL SOLUTION OF FUZZY PARABOLIC DIFFERENTIAL EQUATIONS BY A FINITE DIFFERENCE METHODS". TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 10/4 (2020), 886-896.