Physical Modeling (PM) of musical instruments has gained rising interest over the last decade. This is mainly due to the rising processing capabilities of standard computers making it possible to calculate PM solutions of complete instrument geometries in reasonable computational time or real-time using specialised hardware. Several theoretical advances of discrete solution methods developed over the last 100 years are being explored for PM of musical instruments for the first time. In this work some basic properties of two methods for PM of musical instruments a) Pseudo-Spectral Methods and b) geometry preserving methods known as symplectic (for ODEs) or multisymplectic (for PDEs) are presented and implemented. Two simplified models of musical instruments are presented as a proof of concept.