and the stability of
finite-difference
approximations to IBVP,
410-412,424
Gustafsson-Kreiss-Sundström
(GKS) condition,
409-410
Hennite-cubic polynomials, 226
Heun method, 53
hydrostatic approximation,
372-374
hydrostatic reference state, 23
implicit time-differencing, 53
Jacobian operator, 164
Kreiss matrix theorem, 110
Lagrange iriterpolating polynomial,
204,220,308
Lagrangian form, 303
Lamb wave , 374
Laplacian operator on the sphere,
196-197
Lax equivalence theorem, 40
Lax-Fredrichs method, 102, 254 ,
299-300
Lax-Wendroffmethod,95-99
for the advection-diffusion
equation, 168
for a general conservation law,
98
for the I-D advection
equation, 95-98, 275-276
flux form, 261, 265-272
modified equation
associated with, 104
and semi-Lagrangian schemes,
308
and the Tayler-Galerkin
approximation, 217-219
two-step form of, 96 , 98
for the 2-D advection
equation,98,125-126
Index
461
for 2-D conservation laws ,
281-282,284
leapfrog time-differencing, 57-59,
110-111,343
for the Euler equations,
352-353
and the projection method,
339-340
for semi-Lagrangian schemes,
313,315,320,321
leapfrog-time centered-space
schemes, 92-93
leapfrog-trapezoidal method, 64
Legendre functions, 195, 198
Legendre polynomials, 195,
204-205
Mach number, 21
Magazenkov method, 64-66
mass lumping, 232
mass matrix, 213, 219, 225
matrix nonn, 109
Matsuno's method, 54-56
Me limiter, 268-271 ,300
midpoint method, 54, 61
minmod limiter, 267-271 , 276
modified equation
for the discrete advection
equation, 94-95
for the semi-discrete advection
equation, 81
for the semidiscrete
advection-diffusion
equation, 138
for the Taylor-Galerkin
approximation to the
advection equation,
217-219
monotone method, 251 , 255-256,
292
monotonicity-preserving method,
252-253,292
multigrid method, 342
multistage time-differencing,
53-56