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

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