The simplest form of string synthesis is perhaps the Karplus-Strong algorithm (https://en.wikipedia.org/wiki/Karplus%E2%80%93Strong_string_synthesis https://en.

The simplest form of string synthesis is perhaps the Karplus-Strong algorithm (https://en.wikipedia.org/wiki/Karplus%E2%80%93Strong_string_synthesis https://en.wikipedia.org/wiki/Karplus%E2%80%93Strong_string_...). Instead of simulating the motion of all parts of the string for each timestep, it simplifies it to a perfect transmission of motion, except at the end of the string where some function will be applied that captures the losses from the motion, typically by performing a simple low-pass filter. Computationally it is very efficient: just a few FMA operations per sample. The drawback is that you need a buffer to store the state of the string, which can be quite large (especially for low frequencies which correspond to long strings), and you need to read and write to different parts of this buffer. Thus, if you are simulating multiple strings, it's more likely that memory bandwidth will be the bottleneck instead of raw compute power.