TY - JOUR
T1 - Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type
AU - J. Christy Roja & A. Tamilselvan
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 265
EP - 287
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.y12030
UR - https://global-sci.org/intro/article_detail/nmtma/5875.html
KW - Singularly perturbed problems, third order ordinary differential equations, boundary value technique, asymptotic expansion approximation, shooting method, finite difference
scheme, parallel computation.
AB - <p style="text-align: justify;">In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of convection-diffusion type of third order Ordinary Differential Equations (ODEs) in which the SPBVP is reduced into a
weakly coupled system of two ODEs subject to suitable initial and boundary conditions. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. In order to
get a numerical solution for the derivative of the solution, the domain is divided into
two regions namely inner region and outer region. The shooting method is applied
to the inner region while standard finite difference scheme (FD) is applied for the
outer region. Necessary error estimates are derived for the method. Computational
efficiency and accuracy are verified through numerical examples. The method is
easy to implement and suitable for parallel computing.</p>