Numerical analysis via Chebyshev pseudospectral method for nonlinear initial/boundary value problems

Nader Y. Abd Elazem, Abdelhalim Ebaid

Abstract


In applied science, the physical models are usually described by nonlinear initial/boundary value problems. The exact solutions for such nonlinear models are not always available, the reason that many authors resort to the numerical methods. One of these numerical methods is the Chebyshev pseudospectral method. This method is applied in the current paper to solve some nonlinear initial and boundary value problems of particular interest in applied sciences and engineering. In order to explore the effectiveness and the validity of the present method, many physical models of nonlinear type such as generalized nonlinear oscillator, relativistic oscillator, and Bratu's equations have been solved numerically. The obtained results are compared with other published works through tables and graphs where good accuracy has been achieved.


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How to Cite this Article:

Nader Y. Abd Elazem, Abdelhalim Ebaid, Numerical analysis via Chebyshev pseudospectral method for nonlinear initial/boundary value problems, Journal of Mathematical and Computational Science, Vol 6, No 4 (2016), 597-619

Copyright © 2016 Nader Y. Abd Elazem, Abdelhalim Ebaid. 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.

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