Timestep Control for the Numerical Solutions of Initial-Boundary-Value Problems
The process of dynamic time-step selection for fixed spatial resolution based on the idea of balancing different local truncation errors will be presented. Some theoretical justification and numerical results will also be given. The application of iterative improvement to ADI methods will also be discussed.
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- 2.Douglas, Jr., J., “A survey of numerical methods for parabolic differential equations,” in Advances in Computers, Vol. 2, edited by F. Alt, New York, Academic Press, 1961, pp. 1–54.Google Scholar
- 6.Lindberg, B., “Error estimation and iterative improvement for the numerical solution of operator equations,” UIUCDSD-R-76- 820, Dept. of Computer Science, University of Illinois at Urbana-Champaign (July 1976).Google Scholar
- 10.Tadjeran, Hamid, Ph.D. Dissertation, University of Colorado at Boulder (1980).Google Scholar
- 11.Warming, R.F., and R.M. Bean, “Factored, A-stable, linear multistep methods — an alternative to the method of lines for multidimensions,” Conference Working Paper, 1979 SIGNUM Meeting on Numerical ODEs, Champaign Illinois, ( April, 1979 ).Google Scholar
- 13.Ulam, S., How to formulate mathematically problems of rate of evolution, Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, Symposium Held at the Wistar Institute of Anatomy and Biology, 1966, Ed.: P. Moorhead and M. Kaplan, Wistar Institute Symposium Monograph no. 5, Philadelphia, 1967, 21–23.Google Scholar