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