Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method-Reference-Cited by-同舟云学术

Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method

Published:2015-08-12 Issue:1 Volume:11 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Saha Ray S.¹,Gupta A. K.²

Affiliation:

1. Department of Mathematics, National Institute of Technology, Rourkela 769008, India e-mail:

2. Department of Mathematics, National Institute of Technology, Rourkela 769008, India

Abstract

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.

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4028984/6107067/cnd_011_01_011012.pdf

Reference14 articles.

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2. How to Impose Physically Coherent Initial Conditions to a Fractional System;Commun. Nonlinear Sci. Numer. Simul.,2010

3. Homotopy Perturbation Method: A New Nonlinear Analytical Technique;Appl. Math. Comput.,2003

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