張東凱,田貴辰,鞏增泰,仇計(jì)清

(1.石家莊學(xué)院數(shù)學(xué)與信息科學(xué)系,河北石家莊 050035;2.西北師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,甘肅蘭州 730070;3.河北科技大學(xué)理學(xué)院,河北石家莊 050018)

二階模糊微分方程的數(shù)值解

張東凱1,田貴辰1,鞏增泰2,仇計(jì)清3

(1.石家莊學(xué)院數(shù)學(xué)與信息科學(xué)系,河北石家莊 050035;2.西北師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,甘肅蘭州 730070;3.河北科技大學(xué)理學(xué)院,河北石家莊 050018)

研究了二階模糊微分方程的數(shù)值解,給出并證明了二階模糊微分方程的2個(gè)特征定理,利用特征定理二階模糊微分方程可以轉(zhuǎn)化為微分方程組,從而求得二階模糊微分方程的解。

模糊數(shù);特征定理;模糊微分方程

自從1983年P(guān)URIM等定義模糊微分方程以來(lái)[1],對(duì)其研究越來(lái)越引起學(xué)者們的注意。2005年,GEORGIOU D N等給出了高階模糊微分方程解的存在定理[2]。2008年,ALLAHV IRANLOO T等在廣義可微條件下研究了二階模糊微分方程解的存在定理[3]。文獻(xiàn)[4]中,BEDEB證明了一個(gè)特征定理,利用特征定理能夠?qū)⒁浑A模糊方程轉(zhuǎn)化為微分方程組,從而求得一階模糊微分方程的解。文獻(xiàn)[5]中,PEDERSON S等建立了混合模糊微分方程的特征定理,同樣利用此定理可以將模糊混合微分方程轉(zhuǎn)化為微分方程組,從而求得其解。

在上述研究成果的基礎(chǔ)上,筆者主要討論二階模糊微分方程的數(shù)值解,首先研究了二階模糊微分方程特征定理,利用這些定理,將二階模糊微分方程轉(zhuǎn)化為微分方程組,從而得到了二階模糊微分方程的解,推廣了文獻(xiàn)[4]和文獻(xiàn)[5]的結(jié)果。

1 預(yù)備知識(shí)

2 主要結(jié)論

3 數(shù)值舉例

[1]PURIM,RALESCU D.Differentials of fuzzy functions[J].Journal of Mathematical Analysis and Applications,1983,91:552-558.

[2]GEORGIOU D N,JUAN JN,ROSANNA R L.Initial value p roblems for higher-order fuzzy differential equations[J].Nonlinear Analysis,2005,63:587-600.

[3]ALLAHV IRANLOO T,KIAN IN A,BARKHORDARIM.Toward the existence and uniquenessof solutionsof second-order fuzzy differential equations[J].Information Sciences,2009,179:1 207-1 215.

[4]BEDEB.Note on"Numerical solutions of fuzzy differential equations by p redictor-corrector method"[J].Information Sciences,2008,178:1 917-1 922.

[5]PEDERSON S,SAMBANDHAM M.Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem[J].Information Sciences,2009,179(3):319-328.

[6]DONGKA I Z,WENL I F,JIQING Q.Global existence of solutions to fuzzy volterra integral equations[J].ICIC Exp ress Letters,2009(3B):707-712.

[7]仇計(jì)清,郭彥平.一類復(fù)Fuzzy微分方程的求解[J].河北科技大學(xué)學(xué)報(bào)(Journal of Hebei University of Science and Technology),1998,19(2):12-14.

Numerical solutions to second-order fuzzy differential equations

ZHANGDong-kai1,TIAN Gui-chen1,GONG Zeng-tai2,QIU Ji-qing3
(1.Department of Mathematics and Information Science,Shijiazhuang University,Shijiazhuang Hebei 050035,China;2.College of Mathematics and Information Science,Northwest Normal University,Lanzhou Gansu 730070,China;3.Collegeof Sciences,Hebei U-niversity of Science and Technology,Shijiazhuang Hebei050018,China)

In this paper,we study numerical solutions to second-order fuzzy differential equations initial value p roblems.Two characterization theorems for second-order fuzzy differential equations are given and p roved.Second-order fuzzy differential equations can be translated into ordinary differential equationsby these characterization theorems,so as to obtain solutions to fuzzy differential equations.

fuzzy number;characterization theorem;fuzzy differential equations

O159

A

1008-1542(2010)02-0158-04

2009-10-23;責(zé)任編輯:張 軍

國(guó)家自然科學(xué)基金資助項(xiàng)目(60874003,10771171);石家莊學(xué)院自然科學(xué)基金資助項(xiàng)目(2008)

張東凱(1980-),男,河北平鄉(xiāng)人,講師,碩士,主要從事模糊數(shù)學(xué)與微分方程方面的研究。