We need to consider three cases as it turns out only

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: tudy of heat ﬂow often leads to “boundary-value problems” for ordinary diﬀerential equations. Indeed, in the “steady-state” case, in which u is independent of time, equation (4.5) becomes d dx κ(x) du (x) + µ(x)u(x) + ν (x) = 0, dx 2 A description of the Black-Scholes technique for pricing puts and calls is given in Paul Wilmott, Sam Howison and Jeﬀ Dewynne, The mathematics of ﬁnancial derivatives , Cambridge Univ. Press, 1995. 83 a linear ordinary diﬀerential equation with variable coeﬃcients. Suppose now that the temperature is speciﬁed at the two endpoints of the bar, say u(0) = α, u(L) = β. Our physical intuition suggests that the steady-state heat equation should have a unique solution with these boundary conditions. a. Solve the following special case of this boundary-value problem: Find u(x), deﬁned for 0 ≤ x ≤ 1 such that d2 u = 0, dx2 u(0) = 70, u(1) = 50. b. Solve the following special case of this boundary-value problem: Find u(x), deﬁned for 0 ≤ x ≤...
View Full Document

This document was uploaded on 01/12/2014.

Ask a homework question - tutors are online