# A parameter uniform finite difference method for multiscale singularly
perturbed linear dynamical systems

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0816.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**A parameter uniform finite difference method for multiscale singularly
perturbed linear dynamical systems**

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.