分数阶变系数微分方程的Euler小波解法
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摘要
通过构造Euler小波,推导并利用Euler小波分数阶积分算子矩阵求解一类变系数的分数阶微分方程。研究结果表明,Euler小波方法比其他小波方法具有更高的精度,并且随着参数■的增大,数值解与精确解可以很好地吻合。
In this paper,the Euler wavelet is first constructed and then the Euler wavelet operational matrix of fractional integration derived and used to solve fractional differential equations with variable coefficients.Illustrative example is included to demonstrate the Euler wavelet method which is more accurate than other wavelet methods.The numerical solutions are in very good agreement with exact solution when the value of ■ is increasing.
In this paper,the Euler wavelet is first constructed and then the Euler wavelet operational matrix of fractional integration derived and used to solve fractional differential equations with variable coefficients.Illustrative example is included to demonstrate the Euler wavelet method which is more accurate than other wavelet methods.The numerical solutions are in very good agreement with exact solution when the value of ■ is increasing.
引文
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[2]ZHU L,FAN Q B.Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW[J].Commun.Nonlinear Sci.Numer.Sim.,2013,18(5):1203-1213.
[3]ZHU L,WANG Y X.Solving fractional partial differential equations by using the second Chebyshev wavelet operational matrix method[J].Nonlinear Dynam.,2017,89(3):1915-1925.
[4]BHRAWY A H,ALOFI A S,EZZ S S.A quadrature tau method for fractional differential equations with variable coeffcients[J].Appl.Math.Lett.,2011,24(12):2146-2152.
[5]GARRA R.Analytic solution of a class of fractional differential equations with variable coeffcients by operatorial methods[J].Commun.Nonlinear Sci.Numer.Simul.,2012,17(4):1549-1554.
[6]PODLUBNYI I.Fractional differential equations:an introduction to fractional derivatives,fractional differential equations,to methods of their solution and some of their applications[M].New York:Academic Press,1999:62.
[7]KILICMAN A,ZHOUR Z A A.Kronecker operational matrices for fractional calculus and some applications[J].Appl.Math.Comput.,2007,187(1):250-265.
[8]MING X Y,HUANG J.Wavelet operational matrix method for solving fractional differentialequations with variable coefficients[J].Appl.Math.Comput.,2014,230(1):383-394.