**Finite Difference Methods
for
Ordinary and Partial Differential Equations
**

Steady State and Time Dependent Problems

- p. 23, equation (2.28), $\epsilon$ in both denominators should be
$\epsilon^2$.
- p. 29, line after (2.52), $\beta = 0$ should be $\beta = 3$.
- p. 31, last line, and p. 32, first equation of (2.57): $\sigma$ should be
replaced by $-\sigma$ since the one-sided finite difference approximates
$-u'(x_0)$.
- p. 32, first equation. The
elements of the first row should come from the equation
at the bottom of p. 31, after negating:
$-3h/2,~ 2h,$ and $-h/2$. Also the second and third
rows have an extra 0 (blank) at the start.
(The $-2$ elements should all be on the diagonal.)
The system should be:
$$
\frac{1}{h^2}
\left[
\begin{array}{ccccccccccccccc}
-3h/2 & 2h & -h/2\\
1&-2&1\\
&1&-2&1\\
&&&\ddots\\
&&&&1&-2&1\\
&&&&&0&h^2
\end{array}
\right] ~
\left[
\begin{array}{ccccccccccccccc}
U_0 \\ U_1 \\ U_2 \\ \vdots \\ U_m \\ U_{m+1}
\end{array}
\right]
=
\left[
\begin{array}{ccccccccccccccc}
\sigma \\ f(x_1) \\ f(x_2) \\ \vdots \\ f(x_m) \\ \beta
\end{array}
\right]
$$
- p. 33, equation (2.6), the last part of the equation should be $= u'(0)
+ \int_0^1 f(x) \, dx$.
- p. 130, the last line before section 5.8: "\texttt{typeode45}" should
be "type \textt{ode45}"
- p. 143, the displayed equation between (6.19) and (6.20): The factor
$\frac 5 2$ should be $\frac 1 2$ in the dominant term of the truncation
error.
- p. 158, line -5, "diagonal matrix of eigenvectors" should be
"... eigenvalues".
- p. 172, line -10, the fraction
$\frac{1 - \frac 1 2 k\lambda}{1 + \frac 1 2 k\lambda}$ should be
$\frac{1 + \frac 1 2 k\lambda}{1 - \frac 1 2 k\lambda}$.
- p. 172, line -6,
$(1 + k\lambda)^{-1} \approx - 10^{-6}$ should be
$(1 - k\lambda)^{-1} \approx 10^{-5}$.
- p. 175, equation (8.5): the entry for $r=3: \alpha = 88^\circ$ should
read $r=3: \alpha \approx 86^\circ$ and for $r \geq 4$ the $\alpha = \ldots$
equalities should be $\alpha \approx \ldots$. For $r=6$, $\alpha \approx
17^\circ$ would be on the safer side. See
scholarpedia
article for more precise values.
- p. 222, (10.48): the first $=$ should be $+$.
- p. 321, (E.36) LHS: $\bar{t}$ should be $\bar{x}$
- p. 321, the first sentence below (E.36): $\beta\rightarrow 0$ should be
$\beta\rightarrow +\infty$
- p. 321, the first line below (E.36): $\bar{t}$ should be $\bar{x}$

- p. 8, second line of (1.12),
$\frac{1}{12}$ should be $-\frac{1}{3}$.
- p. 13, line 4: "(ODEs)" should be "(PDEs)"
- p. 23, equation (2.28), $\epsilon$ in both denominators should be
$\epsilon^2$.
- p. 26, line -4: $u_{m+1}=\beta$ should be captial U.
- p. 28, displayed equation in middle of page defining the inf-norm of
$B$: the max should be over $i$, not $j$.
- p. 32, equation (2.57), the first row of the matrix is missing.
To the top of the matrix add a row

[3h/2 -2h h/2 ] - p. 35, line -3: "chain rule" should be "product rule".
- p. 63, in the lines before (3.14), it should refer to the parameters p
and q (not p and k) in two places.
- p. 95: the description of the PCG algorithm is not correct.
In the first unnumbered displayed equation, $w_k$ should be
defined to be $C^T \tilde w_k$ not $C^{-1} \tilde w_k$.
In the algorithm at the bottom of p. 95, the definition of $\alpha_{k-1}$ should have $(z_{k-1}^T r_{k-1})$ in the numerator and the definition of $\beta_{k-1}$ should have $(z_{k-1}^T r_{k-1})$ in the denominator.

The last sentence of this page should then read "... and then use the $z$ vector in place of $r$ in several places in the algorithm."

- p. 121, un-numbered displayed equation between (5.24) and (5.25):
$\frac{1}{12}$ should be $-\frac{1}{3}$.
- p. 130, last sentence of Section 5.7, there should be a space in
"type ode45"
- p. 213, equation (10.29): there is a factor of 1/2 missing in front of
the $\nu$.
- P. 213, equation (10.31): Second line, $+$ sign should be $-$ sign.
the $\nu$.
- P. 213, equation (10.32): First line, $4$ should be $4\nu^2$.
- P. 213, equation (10.33): final term should be $e^{i\xi(j-1)h}$
(remove the minus sign).
- p. 223, equation (10.52): $\nu$ should be $\nu^2$ in last denominator.