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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 , 436451, 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. 3347. New York: Springer-Verlag, 1993. TR BDF2 n 1 n n To integrate du/dt = f ( u ) from t = t n to t n +1 = t n + t n , we first apply the trapezoidal rule (TR) to advance the solution from t n to t n + = t n + t n : u n + - t n 2 f n + = u n + t n 2 f n , (1) and then use the second-order backward differentiation formula (BDF2) to ad- vance the solution from t n + to t n +1 : u n +1- 1- 2- t n f n +1 = 1 (2- ) u n + - (1- ) 2 (2- ) u n . (2) This composite one-step method is second-order accurate and L-stable....
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This note was uploaded on 03/11/2012 for the course MAT 421 taught by Professor Staff during the Fall '11 term at ASU.
- Fall '11