The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE andDAGE have been claimed to be unstable when employed for electrochemical digital simulations withlarge model diffusion coefficient D_M. Howev...The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE andDAGE have been claimed to be unstable when employed for electrochemical digital simulations withlarge model diffusion coefficient D_M. However, in this investigation, in spite of the conditionalstability of GER and GEL, the SAGE scheme, which is a combination of GEL and GER, was found to beunconditionally stable when used for simulations of electrochemical reaction-diffusions and had aperformance comparable with or even better than the Fast Quasi Explicit Finite Difference Method(FQEFD) in some aspects. Corresponding differential equations of SAGE scheme for digital simulationsof various electrochemical mechanisms with both uniform and exponentially expanded space units wereestablished. The effectiveness of the SAGE method was further demonstrated by the simulations of anEC and a catalytic mechanism with very large homogeneous rate constants.展开更多
A new exponential-type weighted implicit difference schcme for solving the Burgers equation was developed and iterated by using the Alternating Group Explicit （AGE） method which has the obvious property of paralleli...A new exponential-type weighted implicit difference schcme for solving the Burgers equation was developed and iterated by using the Alternating Group Explicit （AGE） method which has the obvious property of parallelism. The stability of the method was analyzed with linearization procedure. A model problem was numerically solved with the proposed scheme. The results show that the method is superb or to some existing schemes.展开更多
文摘The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE andDAGE have been claimed to be unstable when employed for electrochemical digital simulations withlarge model diffusion coefficient D_M. However, in this investigation, in spite of the conditionalstability of GER and GEL, the SAGE scheme, which is a combination of GEL and GER, was found to beunconditionally stable when used for simulations of electrochemical reaction-diffusions and had aperformance comparable with or even better than the Fast Quasi Explicit Finite Difference Method(FQEFD) in some aspects. Corresponding differential equations of SAGE scheme for digital simulationsof various electrochemical mechanisms with both uniform and exponentially expanded space units wereestablished. The effectiveness of the SAGE method was further demonstrated by the simulations of anEC and a catalytic mechanism with very large homogeneous rate constants.
基金Project supported by the Teaching and Research Awarded Program for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.China and High Performance Computing Foundation of China (Grant Nos: 99107 ,00108)
文摘A new exponential-type weighted implicit difference schcme for solving the Burgers equation was developed and iterated by using the Alternating Group Explicit （AGE） method which has the obvious property of parallelism. The stability of the method was analyzed with linearization procedure. A model problem was numerically solved with the proposed scheme. The results show that the method is superb or to some existing schemes.
