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Unformatted text preview: TRBDF2 R. E. Bank, W. M. Coughran, W. Fichtner, E. H. Grosse, D. J. Rose, and R. K. Smith, “Transient Simulation of Silicon Devices and Circuits,” IEEE Transactions on Computer-Aided Design , CAD-4 , 436–451, 1985. M. J. Johnson and C. L. Gardner, “An Interface Method for Semiconductor Pro- cess Simulation,” in Semiconductors , IMA Volumes in Mathematics and its Ap- plications, Volume 58, pp. 33–47. New York: Springer-Verlag, 1993. TR BDF2 n 1 n Γ n To integrate du/dt = f ( u ) from t = t n to t n +1 = t n + Δ t n , we first apply the trapezoidal rule (TR) to advance the solution from t n to t n + γ = t n + γ Δ t n : u n + γ- γ Δ t n 2 f n + γ = u n + γ Δ t n 2 f n , (1) and then use the second-order backward differentiation formula (BDF2) to ad- vance the solution from t n + γ to t n +1 : u n +1- 1- γ 2- γ Δ t n f n +1 = 1 γ (2- γ ) u n + γ- (1- γ ) 2 γ (2- γ ) u n . (2) This composite one-step method is second-order accurate and L-stable....
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- Fall '11
- Tn, Numerical ordinary differential equations, Stiff equation, tn n+ tn