Currently, we are using the backward Euler (or implicit Euler) method for the solution of stiff ordinary differential equations during scientific computing.
Assuming a quite performant computer hardware and an identical step size which is smaller than 100us. Are there other stable integration methods that are able to compute
y(n+1) in just one time step (real-time) and have lower truncation errors? What are their pros and cons?
I would like to implement the most promising ones and benchmark their results.