Due to the ever changing characteristics of the newly provided hardware, there is the permanent requirement of designing and redesigning software adequately to meet the basic hardware conditions. Especially for well-established software, easy portability of the functional as well as the non-functional properties, such as runtime performance or energy efficiency, would be beneficial, so that the software adapts automatically to the given hardware conditions. In this article, we explore the autotuning potential of several methods from scientific computing. In particular, we consider time-stepping methods and investigate the effect of relevant tuning parameters of the different methods. We also address the question, whether offline or online autotuning approaches are appropriate for the specific method. The methods from scientific computing considered are particle simulation methods, solution methods for differential equations, as well as sparse matrix computations. Index Terms-offline and online autotuning, performance analysis, portability of efficiency, time-stepping methods.