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

Randall J. LeVeque

Errata for the first printing

• p. 13, line 4: "(ODEs)" should be "(PDEs)"

• 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. 47, second line of (2.96), $W'$ should be $W''$.

• p. 63, in the lines before (3.14), it should refer to the parameters q 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 page 95 should then read "... and then use the $z$ vector in place of $r$ in several places in the algorithm."

• p. 130, last sentence of Section 1.30, 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. 216, line 10: $u(X-aT)$ should be $\eta(X-aT)$

• 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.