Hi, Christophe, I get the 2nd resolution (Wave_t_ex) run successfully according to my understanding in my last email to you. It seems the solution is smoother than that with the 1st resolution. Is it expected that way or it is just an individual case? I still need you help me with the other questions. Best wishes, Lin -- Dept. of Math., RPI 518-276,2184(work) 518-271,4486(home)