Numerical solution of non-linear partial differential equation for porous media using operational matrices

Shubham Jaiswal, Manish Chopra and S. Das

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 160, issue C, 138-154

Abstract: Nonlinear partial differential equations (NPDEs) play a significant role in modeling of many complex physical problems and engineering processes. Development of reliable and efficient techniques to solve such types of NPDEs is the need of the hour. In this article, numerical solutions of a class of NPDEs subject to initial and boundary conditions are derived. In the proposed approach, shifted Chebyshev polynomials are considered to approximate the solutions together with shifted Chebyshev derivative operational matrix and spectral collocation method. The benefit of this method is that it converts such problems in the systems of algebraic equations which can be solved easily. To show the efficiency, high accuracy and reliability of the proposed approach, a comparison between the numerical results of some illustrative examples and their existing analytical results from the literature is reported. There is high consistency between the approximate solutions and their exact solutions to a higher order of accuracy. The error analysis for each case exhibited through graphs and tables confirms the super-linear convergence rate of the proposed method.

Keywords: Burgers equation; Fisher equation; Huxley equation; Shifted Chebyshev polynomials; Collocation method (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475418303264
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:160:y:2019:i:c:p:138-154

DOI: 10.1016/j.matcom.2018.12.007

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().