JAMC
Numerical Simulation of a Singularly Perturbed Harmonic Oscillator
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Abstract
A singular perturbation problem is a differential equation such that the coefficient of the higher order derivative is significantly smaller than that of the lower one. As a result, the solution of such a differentiation displays the nonuniform continuity which requires special numerical treatment. Singular perturbation arises in many physical applications. A mass-spring system with a small mass forms a singularly perturbed damped harmonic oscillator. In a short time period, the spring oscillates rapidly and displays a boundary layer because of the small mass. Then the oscillation becomes smooth and it can be approximated in the absence of the small mass. An adaptive piecewise uniform numerical simulation scheme is proposed. On the non-boundary layer, it is approximated by the classical numerical approximation and on the boundary domain, it is solved with the adaptive scheme according to the singular perturbation parameter. The accuracy is achieved at a high level with a constant number of mesh points for a family of singularly perturbed harmonic oscillators.
Keywords
Singular Perturbation, Oscillator, Differential Equations, Numerical Methods
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How to cite this paper
Numerical Simulation of a Singularly Perturbed Harmonic Oscillator
How to cite this paper: Weiqun Zhang. (2023) Numerical Simulation of a Singularly Perturbed Harmonic Oscillator. Journal of Applied Mathematics and Computation, 7(2), 243-248.
DOI: http://dx.doi.org/10.26855/jamc.2023.06.005
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