March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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Chapter 7
Numerical Solution of Differential
Equations
Differential equations relate a function f to its derivatives. They play a very
important role in science and engineering and arise in a wide range of appli-
cations.
Example 7.1 In finance, a bond is a fixed-income security that can be de-
scribed using the following attributes [22]: current price P ; coupon payment
rate c; the number of coupon payments per year m; the number of years to
maturity n; yield to maturity λ–the annual interest rate that is implied by
the current price; and the modified duration D
M
, which is computed by the
following formula:
D
M
= D
M
(c, m, n, λ)=
1
λ
−
1+nc − (mn − 1)λ/m
(1 + λ/m
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