2009-106.md

course	course_year	question_number	tags	title	year
Numerical Analysis	II	106	II 2009 Numerical Analysis	Paper 4, Section II, B	2009

(a) For the $s$-step $s$-order Backward Differentiation Formula (BDF) for ordinary differential equations,

$$\sum_{m=0}^{s} a_{m} y_{n+m}=h f_{n+s}$$

express the polynomial $\rho(w)=\sum_{m=0}^{s} a_{m} w^{m}$ in a convenient explicit form.

(b) Prove that the interval $(-\infty, 0)$ belongs to the linear stability domain of the 2-step BDF method.