# How to isolate and test time discretization order of accuracy

I have a code that uses both spatial and time discretization/integration. For convergence analysis, I am wondering how one would test the order of accuracy of their ${time}$ integration scheme? I assume you would have to isolate the time discretization from the spatial discretization somehow, but I am not sure how this can be done on a discretized mesh. I suppose you could choose some really really small spatial step size such that the spatial error is less than the time error, but this seems very inelegant and complicated.

• What are you considering as the truth in your analysis? – origimbo Jun 7 '18 at 22:12
• I'm taking "truth" to mean an 'exact' solution. If that's correct, then the truth is a manufactured solution (I'm using the method of manufactured solutions). – user27504 Jun 8 '18 at 0:51

• I understand. Would this method work to determine the order of accuracy of my time integration method, by comparing my numerical solution to a hypothetical exact solution, where the hypothetical exact solution is just the solution obtained using some very small $\Delta t$? – user27504 Jun 8 '18 at 17:25