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Stabilize the Oscillations using Leapfrog Method
Fatin Amierah Binti Zailani
Supervisor: Dr. Ilyani Binti Abdullah
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Oscillations occur not only in physical systems but also in biological systems and in human
society. The simplest mechanical oscillating system is a mass, subject to the force of
gravity, attached to a linear spring. Thus, not all the oscillations are stable. To stabilize
the oscillations, leapfrog method was used to solve this problem. The leapfrog method
which is second order, is closely related to a modification of the Euler method called
Euler-Cromer. However, the Euler method is an energy increasing method. This means
that as iterate over time, the sequence of solutions will produce an increasing numerical
oscillations. Since each updated solution will have more and more oscillations, the energy
of the system will increase artificially. This method is popular because it is more accurate
over a longer time-iteration range. We call this a stable method.
924 | UMT UNDERGRADUATE RESEARCH DAY 2018