Discussion of “Elimination of Overshoot in Forced Vibration Responses for Chang Explicit Family Methods” by Shuenn-Yih Chang
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References
Bathe, K. 1982. Finite element procedures in engineering analysis. Englewood Cliffs, NJ: Prentice Hall.
Butcher, J. 1987. “The Euler method and its generalizations.” In The numerical analysis of ordinary differential Equations: Runge-Kutta and general linear methods, 105–151. New York: Wiley.
Butcher, J. 2005. “Numerical differential equation methods.” In Numerical methods for ordinary differential equations, 45–121. New York: Wiley.
Chang, S. 2010. “A new family of explicit methods for linear structural dynamics.” Comput. Struct. 88 (11–12): 755–772. https://doi.org/10.1016/j.compstruc.2010.03.002.
Dahlquist, G. 1963. “A special stability problem for linear multistep methods.” BIT Numer. Math. 3 (1): 27–43. https://doi.org/10.1007/BF01963532.
Har, J., and K. Tamma. 2012. Advances in computational dynamics of particles, materials and structures. New York: Wiley.
Lambert, J. 1973. Computational methods in ordinary differential equations. New York: Wiley.
Tamma, K. K., J. Har, X. Zhou, M. Shimada, and A. Hoitink. 2011. “An overview and recent advances in vector and scalar formalisms: Space/time discretizations in computational dynamics—A unified approach.” Arch. Comput. Methods Eng. 18 (2): 119–283. https://doi.org/10.1007/s11831-011-9060-y.
Tamma, K. K., X. Zhou, and R. Kanapady. 2002. “The time dimension and a unified mathematical framework for first-order parabolic systems.” Numer. Heat Transfer: Part B: Fundam. 41 (3–4): 239–262. https://doi.org/10.1080/104077902753541005.
Tamma, K. K., X. Zhou, and D. Sha. 2000. “The time dimension: A theory towards the evolution, classification, characterization and design of computational algorithms for transient/dynamic applications.” Arch. Comput. Methods Eng. 7 (2): 67–290. https://doi.org/10.1007/BF02736209.
Wood, W. 1990. Practical time-stepping schemes. Oxford, UK: Oxford University Press.
Zhou, X., and K. Tamma. 2004a. “Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics.” Int. J. Numer. Methods Eng. 59 (5): 597–668. https://doi.org/10.1002/nme.873.
Zhou, X., and K. Tamma. 2004b. “A new unified theory underlying time dependent linear first-order systems: A prelude to algorithms by design.” Int. J. Numer. Methods Eng. 60 (10): 1699–1740. https://doi.org/10.1002/nme.1019.
Zhou, X., K. Tamma, and D. Sha. 2005. “Design spaces, measures and metrics for evaluating quality of time operators and consequences leading to improved algorithms by design-illustration to structural dynamics.” Int. J. Numer. Methods Eng. 64 (14): 1841–1870. https://doi.org/10.1002/nme.1405.
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©2019 American Society of Civil Engineers.
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Received: Mar 28, 2018
Accepted: Aug 24, 2018
Published online: Aug 28, 2019
Published in print: Nov 1, 2019
Discussion open until: Jan 28, 2020
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