Although circuit analysis programs have a long tradition as standard CAD tools and have been successfull for an extremely wide range of applications, their algorithms should be improved with respect to reliability, efficiency and functionality. This paper surveys shortly some common problems and possible solutions associated with: convergence of operating point analysis, damping of numerical integration, exploitation of latency, and standard frequency analysis; also speedups due to vectorization are discussed. The basic ideas behind the solutions are not really new, rather they are taken over from mathematical literature and/or adopted for the use in an industrial circuit simulator. The algorithms are implemented in the program TITAN which was developed for inhouse use at Siements' research laboratories. For each topic practical examples are given in order to illustrate the progress in comparison with classical circuit simulation.