Finite difference methods for vibration problems

Authors:Hans Petter Langtangen Date:Nov 12, 2014

Note: PRELIMINARY VERSION (expect typos)

Vibration problems lead to differential equations with solutions that oscillate in time, typically in a damped or undamped sinusoidal fashion. Such solutions put certain demands on the numerical methods compared to other phenomena whose solutions are monotone. Both the frequency and amplitude of the oscillations need to be accurately handled by the numerical schemes. Most of the reasoning and specific building blocks introduced in the fortcoming text can be reused to construct sound methods for partial differential equations of wave nature in multiple spatial dimensions.