Finite Difference Methods for Ordinary and Partial Differential Equations
Steady State and Time Dependent Problems

### Errata for books published after mid-2010

• 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 $\bar{x}$

### Errata for books published before mid-2010

• 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.