This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which t...This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.展开更多
基金The work of this author is supported in part by E-Institutes of Shanghai Municipal Education Commission （No. E03004）, Shanghai Science and Technology Commission （No.03QA14036）, Shanghai Leading Academic Discipline Project （No. T0401）, Science Foundation of Shanghai （No. 04JC14062） and Special Funds for Major Specialties of Shanghai Education Commission.Acknowledgement. The authors wish to thank the anonymous referees for their carefully correcting the preliminary version of the manuscript.
文摘This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.
