MAE 05 UCSD

1 MAE290a midterm (2005) 75 minutes, closed book, no calculators, one page of notes allowed. 1. Dene 1 1 0 00 1 2 1 0 0 0 1 2 1 0 , A= 0 0 1 2 1 0 0 0 01 0 0 b = 0 . 0 1 a) Using the Gaussian elimination procedure discussed in class, nd

1 MAE290a nal (2005) 3 hours, closed book, no calculators, two pages of notes allowed. 1. Adams-Moulton methods We have seen in class a variety of methods to integrate the ordinary differential equation dy = f(y,t) with y(t0 ) = y0 . dt Most of the

1 MAE290a nal solutions (2005) 1. Adams-Moulton (AM) methods (1A) This implicit method is well suited for linear problems f(y) = Ay for which A has tightly banded sparsity. (1B) (0 h 1)2 + (1 h + 1) + (2h) = 0. (1C) For stability, we need |+ | 1 a

1 MAE290a nal solutions (2005) 1. Adams-Moulton (AM) methods (1A) This implicit method is well suited for linear problems f(y) = Ay for which A has tightly banded sparsity. (1B) (0 h 1)2 + (1 h + 1) + (2h) = 0. (1C) For stability, we need |+ | 1 a

1 MAE290a nal (2005) 3 hours, closed book, no calculators, two pages of notes allowed. 1. Adams-Moulton methods We have seen in class a variety of methods to integrate the ordinary differential equation dy = f(y,t) with y(t0 ) = y0 . dt Most of the

1 MAE290a midterm (2005) 75 minutes, closed book, no calculators, one page of notes allowed. 1. Dene 1 1 0 00 1 2 1 0 0 0 1 2 1 0 , A= 0 0 1 2 1 0 0 0 01 0 0 b = 0 . 0 1 a) Using the Gaussian elimination procedure discussed in class, nd