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Chapters
Continuous Modeling and Simulation
Heat Transfer: Model and Numerical Solution
Numerics of PDE

Numerics of PDE

← PreviousModeling with PDE

Next →Appendix

Index

A

abstract model
accuracy
admissible schedule
admissible schedule (job-shop)
alternative-caution strategy (min-max regret)
analytic solution
approximate-numerical method
arbitrary machines
arc length
arms race of two superpowers
Arrow's impossibility theorem
asymmetric (relation)
attractive equilibrium
augmented precedence graph

B

best response function
bijective function
binary relation
boundary
boundary point
boundary value problem (BVP)
bounded set

C

carrying capacity
Cartesian coordinates
caution strategy (max-min payoff)
change of variables
characteristic polynomial
Cᵏ class
Cᵏ-curve
closed curve
closed set
closure
collective choice function
compact set
conjunctive edge
connex
continuity (multivariate function)
continuous model
continuously partially differentiable
convergence (vector sequence)
convex set
coordinate transformation
coordinate transformation matrix
critical path
Critical Path Method (CPM)
critical vertex
cross product
cross-product matrix
curve
cylindrical coordinates

D

DAG (directed acyclic graph)
data error
decision under certainty
decision under risk
decision under uncertainty
definite integral
definiteness of a symmetric matrix
determinant (2×2)
determinant (3×3)
determinant from eigenvalues
deterministic model
diagonal matrix
difference quotient
differentiable (multivariate)
differentiation rules
direct-numerical method
directional derivative
directional field
discrete model
discretization
discretization error
discriminant
disjunctive edge
disjunctive edge assignment
divergence
double integral (rectangular domain)
double integral (standard domain)
doubling time

E

eigenvalue and eigenvector
eigenvalues of a diagonal matrix
embed-test definition
embed-test theorem
equilibrium point
Euclidean norm
expected payoff (mixed strategies)
external dictator

F

floating-point number
Fubini's theorem
full-risk strategy (max-max payoff)
fundamental theorem of calculus

G

Gauss's divergence theorem
generic decision model
global extremum
gradient
growth rate

H

Hessian matrix
heuristic

I

ideal arithmetic
identical machines
identity matrix
ill-posed problem
image (trace) of a curve
independence of irrelevant alternatives
initial value problem (IVP)
injective function
inner point
inner product
inner product (geometric form)
instationary (PDE)
integration by parts
integration rules
interior
internal dictator
inverse problem
isoline

J

Jacobian determinant
Jacobian matrix
job-shop model

K

k-times continuously partially differentiable

L

Laplace operator
lead time
linear 1st-order PDE (in 2D)
linear birth and death rates
linear PDE
local convergence of Newton's method
local extremum
logistic growth model

M

majority decision
makespan
Malthus model
mathematical modeling
minimax theorem
mixed strategy
model
model hierarchy
multiscale problem
multivariate function

N

nabla operator
Newton iteration (multivariate)
no-dictator condition
nullcline

O

open set
ordinary differential equation (ODE)

P

Pareto condition
partial derivative
partial differential equation (PDE)
partially differentiable
pessimism–optimism strategy (Hurwicz)
phase portrait
piecewise C¹-curve
plane curve
polar coordinates
practical model
precedence condition
precedence graph
preference relation
principle of insufficient reason (Laplace)
priority-list scheduling

Q

q-th moment
quadratic formula
qualitatively identical machines
quasi-order
quasilinear 1st-order PDE (in 2D)

R

rank addition
rank mapping
reflexive (relation)
regret
regular surface
remaining time
repulsive equilibrium
resolution (floating-point)
root
rotation
round-off error
rounding

S

T

tangent vectors
Taylor polynomial
theorem of underestimation (Fulkerson 1962)
topological sort
trace
trace from eigenvalues
trajectory
transitive (relation)
translation invariance (differentiation)
transpose
trigonometric derivatives
trigonometric integrals
triple integral (box domain)
triple integral (standard domain)
truncation error
two-player zero-sum game
two-species model

V

validation
vector field
vector projection
vector surface integral
Verhulst saturation model
Vieta's formulas
voting paradox

W

well-posed problem

#

1st-order linear PDE with constant coefficients
ε-ball

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