TY - JOUR
T1 - A Parameter-Uniform Finite Difference Method for Singularly Perturbed Linear Dynamical Systems
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 535
EP - 548
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/736.html
KW - Linear dynamical system, multiscale, initial value problem, singularly perturbed, finite difference method, parameter-uniform convergence.
AB - <p style="text-align: justify;">A system of singularly perturbed ordinary differential equations of
first order with given initial conditions is considered. The leading term of each
equation is multiplied by a small positive parameter. These parameters are
assumed to be distinct and they determine the different scales in the solution
to this problem. A Shishkin piecewise-uniform mesh is constructed, which is
used, in conjunction with a classical finite difference discretization, to form a
new numerical method for solving this problem. It is proved that the numerical
approximations obtained from this method are essentially first order convergent
uniformly in all of the parameters. Numerical results are presented in support
of the theory.</p>