Numerical Analysis
2015 Fall
Numerical Methods
Model Function
dv
dt g
cd
mv2
v t gm
cdtanh
gcd
mt
Analytical solution
Numerical solution
)( 1
2
1 iiid
ii tttvm
cgtvtv
Model Function
Numerical solution
)( 1
2
1 iiid
ii tttvm
cgtvtv
Euler’s method : given initial value, solve diff. eq. using first order numerical procedure
Next = present + slope time step
Bases for Numerical Models • Conservation laws provide the foundation for
many model functions.
• Different fields of engineering and science apply these laws to different paradigms within the field.
• Among these laws are:
Conservation of mass
Conservation of momentum
Conservation of charge
Conservation of energy
Bases for Numerical Models
Change = increase – decrease
Change = 0 = increase – decrease
increase = decrease
Types of balances
Problem 1-9
Volume change = increase – decrease
QtQ
dt
Ayd 2sin3
)(
A
Qt
A
Q
dt
dy 2sin3
Euler’s
method
Problem 1-9
A
Qt
A
Q
dt
dy 2sin3 Next = present + slope time step
Numerical Methods
Pattern Detection
Numerical Methods
Homography
Numerical Methods
Superresolution
Numerical Methods
Surface Normal (point local structure)
Numerical Methods
Tracking