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This work deals with the
numerical solution of singular perturbation system of ordinary differential
equations with boundary layer. For the numerical solution of this problem
fitted finite difference scheme on a uniform mesh is constructed and analyzed.
The uniform error estimates for the approximate solution are obtained.
A glance at Bessel
functions shows they behave similar to the damped sinusoidal function. In this
paper two physical examples (pendulum and spring-mass system with linearly
increasing length and mass respectively) have been used as evidence for this
observation. It is shown in this paper how Bessel functions can be approximated
by the damped sinusoidal function. The numerical method that is introduced
works very well in adiabatic condition (slow change) or in small time
(independent variable) intervals. The results are also compared with the