I found that there are serious differences in 2nd order approximation simulation results between using Dynare++1.3.5 and Dynare v3. I used all same model with same standard deviations. If I used 2nd order apporximation for each cases, the simulation results should be same. Am I right?

you are perfectly perfectly right (almost as my wife).

If you attach the example and tell where exactly are the differences, we could debug it.

Please, note that dynare++ calculates simulated ergodic distribution, but dynare calculates 2nd order accurate ergodic distribution for 2nd order accurate solution (called “theoretical mean and variance”). In future, I will add calculation of m-th order accurate ergodic distribution for k-th order accurate solution (where m and k might be different) to dynare++.