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Research Papers

Wavelet Method for a Class of Fractional Klein-Gordon Equations

[+] Author and Article Information
G. Hariharan

Department of Mathematics,
School of Humanities and Sciences,
SASTRA University,
Thanjavur-613 401, Tamilnadu, India
e-mail: hariharan@maths.sastra.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 12, 2011; final manuscript received May 10, 2012; published online July 23, 2012. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(2), 021008 (Jul 23, 2012) (6 pages) Paper No: CND-11-1216; doi: 10.1115/1.4006837 History: Received December 12, 2011; Revised May 10, 2012

Wavelet analysis is a recently developed mathematical tool in applied mathematics. A wavelet method for a class of space-time fractional Klein–Gordon equations with constant coefficients is proposed, by combining the Haar wavelet and operational matrix together and efficaciously dispersing the coefficients. The behavior of the solutions and the effects of different values of fractional order α are graphically shown. The fundamental idea of the Haar wavelet method is to convert the fractional Klein–Gordon equations into a group of algebraic equations, which involves a finite number of variables. The examples are given to demonstrate that the method is effective, fast, and flexible; in the meantime, it is found that the difficulties of using the Daubechies wavelets for solving the differential equation, which need to calculate the correlation coefficients, are avoided.

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Topics: Wavelets
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Figures

Grahic Jump Location
Fig. 3

Absolute error for α=0.5,    t=0.5 s and different values of m = 16 for Example 1

Grahic Jump Location
Fig. 2

Comparison between the exact and the Haar solution for Example 1 and m = 64

Grahic Jump Location
Fig. 1

Numerical solution of u(x,t) corresponding to the value of α=0.01 and m = 16

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