Index
(,)h scalar product
D+, D−, D0
eigenfunctions and eigenvalues
D+D−
L2-norm
L2-scalar product
|| ||h norm
1-periodic function
a priori estimates
accuracy
local
local and global
of the computed computed
Adams methods
Adams-Bashforth methods
Adams-Moulton methods
amplification factor
amplitude
artificial dissipation
fourth order
asymptotic expansion
boundary conditions
1-periodic
Dirichlet
mixed
Neuman homogeneous
boundary locus method
CFL condition
characteristic equation
difference operator
backward
centered
forward
fourth order accurate
Duhamel’s principle
discrete
energy
discrete case
heat equation
one-way wave equation
energy estimate
Euclidean inner product
Euclidean norm
Euler method
explicit
implicit
improved
stability
existence and uniqueness
for ODEs
for semidiscrete problem
extrapolation
fast Fourier transform
direct (FFT)
inverse (IFFT)
forced solution
forcing
Fourier interpolation
Fourier series
ghost points
Gibbs phenomenon
grid
function
point
heat equation
backward
on a strip
semidiscrete
Heun method
illposed
incoming wave
increment function
initial layer
integration by parts
Lax-Wendroff method
leapfrog method
modified
limit layer (discrete)
linearized equation
local error
localization
lower-order terms
matrix norm
subordinate
method of lines
one-step method
one-way wave equation
on a strip
semidiscrete
order of accuracy
outgoing wave
parabolic problem
general
Parseval’s relation
discrete
particular solution
phase
error
precision quotient
predictor-corrector
principal part
principle of frozen coefficients
principle of linearization
problem
stable
strongly stable
unstable
Runge-Kutta method
classical fourth order
order p
order
solution expansion
solution operator
span
stability
conditional
leapfrog
stability condition
stability region
4th order Runge-Kutta
explicit Euler
improved Euler
leapfrog
multistep methods
one-step method
step size
variable
stiff equation
summation by parts
superposition principle
Taylor method
second order
transient solution
trapezoidal rule
truncation error
Euler method
Lax-Wendroff
leapfrog
one-step method
uniqueness
wave equation
on a strip
semidiscrete
well posed
strongly
system
3.14.131.212