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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 105414, 6 pages
http://dx.doi.org/10.1155/2014/105414
Research Article

A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations

1Department of Basic Sciences and Humanities, EME College, National University of Sciences and Technology (NUST), Peshawar Road, Rawalpindi 46000, Pakistan
2Department of Mathematics, Statistics and Physics, Qatar University, P.O. Box 2713, Doha, Qatar
3School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan

Received 24 April 2014; Revised 7 July 2014; Accepted 8 July 2014; Published 22 July 2014

Academic Editor: Bashir Ahmad

Copyright © 2014 Mazhar Iqbal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.