In this paper, the numerical solution for the fractional order partial differential equation (PDE) of parabolic type has been presented using two dimensional (2D) Legendre wavelets method. 2D Haar wavelets method is also applied to compute the numerical solution of nonlinear time-fractional PDE. The approximate solutions of nonlinear fractional PDE thus obtained by Haar wavelet method and Legendre wavelet method are compared with the exact solution obtained by using homotopy perturbation method (HPM). The present scheme is simple, effective, and expedient for obtaining numerical solution of the fractional PDE.
Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method
National Institute of Technology,
Rourkela 769008, India
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 20, 2014; final manuscript received October 30, 2014; published online August 12, 2015. Assoc. Editor: J. A. Tenreiro Machado.
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Saha Ray, S., and Gupta, A. K. (August 12, 2015). "Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method." ASME. J. Comput. Nonlinear Dynam. January 2016; 11(1): 011012. https://doi.org/10.1115/1.4028984
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