Page 18, line 3: replace intesting by interesting

Page 62, line 6: replace right-hand-side by right-hand side

Page 69, equation (2.35): replace $=a,$ by $=s,$

Page73, line 6: replace (t,x) by (t,x_1)

Page 81, first line of Sect. 3.1: replace rigious by regions

Page 112, in Neumann and Robin conditions: replace $k$ by $D$

Page 112, line -10: replace parabolic methods by parabolic equations

Page 113, line 16: replace One-dimensional case, central approximation by One-dimensional case

Page 116, line 13: replace $x<1$ by $x>0$

Page 135, line 2: replace $u^2$ by $u_2$

Page 136, line 15: replace $=$ by $\cong$

Page 150, line -7: replace ever though by even though

Page 155, line 2: replace ...following form: by ...following form, following Spekreijse (1987):
[Spekreijse, S.P. (1987). Multigrid Solution of Monotone Second-Order Discretizations of Hyperbolic Conservation Laws. Math. Comp.  49, 135-155]

Page 159, third equation: replace $(f,($ by $(f_1($

Page 166, equation (5.11): replace the last two instances of $\varphi$ by $q$.

Page 168, lines 3 and 10: replace such that by such that for arbitrary $\delta^0$

Page 178, equation before equation (5.45): replace $c^4$ by $c_{\alpha}^4$

Page 179, first equation: replace = by <=

Page 182, eqs. (5.61), (5.62) and (5.63): replace $(\sum$ by $\sum ($

Page 182, after eq. (5.62), in formula for $\tilde{q}_1$, replace $(\frac{5+\sqrt{10}}{12})$ by $(\frac{5+\sqrt{10}}{12})^{1/3}$

Page 219, first line: replace $yn$ by $y^n$

Page 234, line 10: delete character 2 at beginning of this line

Page 252, line 11: replace ponts by points

Page 252, line -10: replace rhe by the

Page 257, line 7: replace $(\sum_{\alpha} u^4_{\alpha}/h^2_{alpha})^{-1/3}$ by
$/ \sum_{\alpha} (u^4_{\alpha}/h^2_{alpha})^{1/3}$

Page 266, in definition 7.2.2, replace $i \not= i$ by $i \not= j$

Page 277, in algorithm Preconditioned GMRES method:
insert the following statement after $h_{kj} = (v^k,w);$:
$w = w - h_{kj}v^k);$

Page 282, equation (7.31): delete: $\tilde{y} = C^{-T},$

Page 284, last line: replace $y = C^{-1}\tilde{y}$ by $y = C\tilde{y}$

Page 285, line 5: replace a by A

Page 296, line 4: replace inamely by namely

Page 317, after equation (8.36): replace = by \leq (less or equal)

Page 363, first equation, replace first occurrence of $f$ by $\phi$

Page 382, line 16: delete: Riemann!approximate solver

Page 385, line -14: replace $a_j$ and $\varphi_j$ by $a_j$ and $b_j$

Page 429, line -9: replace $=c_1/c_0\equiv\alpha$ by $ = (c_1/c_0)(p_0/p_1)^{(\gamma -1)/(2\gamma)}\equiv\alpha$

Page 459 The van Albada limiter corresponds to $\kappa = 0$ and not to $\kappa = 1/2$, see Sect. 4.8. Therefore line 21 and equation (10.108) should be replaced by:
This gives, with $\kappa = 0,$
$\lambda < \lambda_1 = 0.9/\bar{\mu}.$

Page 466: According to the erratum for page 458, Table 10.4 should be redone for $\kappa = 0: \lambda_1 = 0.9/\bar{\mu}.$

Page 579, line 13: replace $\varepsilon$-dependent time by $\sqrt{\varepsilon}$-dependent time

Page 591, last line of equation (14.36): add the following term to the right-hand side: $ - \lambda T_{j}^{n} [(1-s^{n})m^{*}] |_{j-1/2}^{j+1/2}$