Home
Add Document
Sign In
Register
Numerical Methods Formula Sheet
Home
Numerical Methods Formula Sheet
numec formulaFull description...
Author:
Muhammad Asyraaf Anuar
6 downloads
429 Views
384KB Size
Report
DOWNLOAD .PDF
Recommend Documents
Numerical Methods Formula Sheet
Descripción: numec formula
Numerical Methods Formula Sheet
Numerical Methods Formula SheetFull description
Numerical Methods Formula Sheet - Copy
Numerical Methods Formula Sheet - CopyFull description
Numerical Methods
Numerical Methods
Numerical Methods
Numerical Methods in Electromagnetics
Numerical Methods in Electromagnetics
Numerical Methods Viva
Numerical Methods MCQ
NM
Numerical-Methods-E-Balaguruswamy.pdf
Numerical Methods in Geomechanics
Full description
Numerical Methods E Balaguruswamy
Full description
Jain Iyengar Numerical Methods
Numerical Methods in Engineering
Matlab Jaan Kiusalaas Solution Manual
Numerical-Methods-E-Balaguruswamy.pdf
Full description
Numerical Methods in Engineering
Matlab Jaan Kiusalaas Solution Manual
Numerical Methods 6th Chapra
212C Numerical Methods
MCQs on numerical methods
Numerical Methods for Engineers
Introduction about roots of equation
Numerical Methods E Balaguruswamy
Full description
Formula sheet
ere4tW
Numerical Method Cheat Sheet
Gate Numerical Methods Cheat Sheet
Numerical Methods for Electrical Engineers
Descripción: Problem Solving in Numerical Methods
Multiple Choice Questions Numerical Methods
Multiple Choice Questions Numerical Methods
FORMULA SHEET FOR NUMERICAL METHODS FOR ENGINEERS COEB223 / MATB324
Part 1: Modeling, Computers and Error Analysis Error Definitions True error: True percent relative error:
Approximate percent relative error:
Stopping criterion: Terminate computation when εa < εs where εs is the desired percent relative error
Taylor Series Taylor series expansion (
)
( )
( )
( )
( )(
( )
)
where remainder (
)(
(
)
)
(
or
)
Error propagation For n independent variables x1, x2, …, xn having errors ̃ ,
̃ , …,
function f can be estimated via |
| ̃
|
| ̃
Page 1 of 8
|
| ̃
̃ , the error in the
COEB223 / MATB324 Formula Sheet
Part 2: Roots of Equations Method
Formulation
Bisection
( )( ( )
False Position
(
) )
If ( )
( )
set
If ( )
( )
set
If ( )
( )
set
If ( )
( )
set
( ) ( )
Newton Raphson
Secant
( )( ( )
) ( )
Part 3: Linear Algebraic Equations Gauss Elimination
[
]
[
]
LU decomposition Back Substitution
Decomposition
[
]
[
]{
}
{ }
[
]{ }
Forward Substitution
Page 2 of 8
{
}
{ }
COEB223 / MATB324 Formula Sheet
Gauss-Seidel method
|
|
} With relaxation, (
)
Part 4: Curve Fitting Method Linear Regression
Formulation
Errors √
where )
∑( ∑ ∑
∑ ∑ (∑ )
where: ∑(
Polynomial Regression
̅)
For a 2nd order polynomial fit, √
(
)
where )
∑(
by differentiating Sr with respect to each coefficients and setting the partial derivatives equal to zero, we have: ∑
∑
∑
∑
∑
[∑
∑
∑
∑ { ]
}
∑ {∑
Page 3 of 8
}
where: ∑(
̅)
COEB223 / MATB324 Formula Sheet
Multiple Linear Regression
√
(
)
For a two-variable linear fit,
where where:
)
∑(
∑( by differentiating Sr with respect to each coefficients and setting the partial derivatives equal to zero, we have: ∑ ∑ [∑
Newton’s divided difference interpolating polynomial
∑
∑
∑
∑
∑
{
∑
}
{∑
]
}
For third order: ( )
(
) (
( )(
)( )(
where ( ) [
]
[ [ Lagrange interpolating polynomial
∑
( )
∑
] ]
( ) ( )
where, ( )
∏
Page 4 of 8
) )
̅)
COEB223 / MATB324 Formula Sheet
Part 6: Numerical Differentiation and Integration A. Numerical Differentiation Method Forward finitedivided difference
Formulation First Derivative: (
( )
( )
( ) )
(
)
( ) (
)
First Derivative: ( )
( )
(
( )
( )
Centred finitedivided difference
) (
( )
Backward finitedivided difference
Errors
( )
) (
)
(
) (
)
(
)
(
)
First Derivative (
( )
)
(
(
( )
)
) (
)
(
)
(
B. Numerical Integration Method
Formulation
Trapezoidal rule
(
)
Multiple-application trapezoidal rule
(
)
( )
( )
( ( )
Page 5 of 8
∑ ( )
(
))
)
COEB223 / MATB324 Formula Sheet
Simpson’s 1/3 rule
Multiple-application Simpson’s 1/3 rule
Simpson’s 3/8 rule
Gauss Quadrature
(
)
(
)
(
)
( )
( )
( )
( ( )
( )
( )
( )
∑
( )
( )
( )
(
∑
( )
)
Gauss-Legendre For two-point Gauss-Legendre:
For three-point Gauss-Legendre:
Change of variables: (
Page 6 of 8
)
(
)
( )
(
))
COEB223 / MATB324 Formula Sheet
Part 7: Ordinary Differential Equations Method
Formulation
Euler’s First-Order RK (
Heun’s Second Order RK
)
(
)
(
)
(
)
Midpoint Second Order RK (
)
(
Ralston’s Second Order RK
)
(
)
(
)
(
Classical Fourth Order RK
)
( (
) )
(
)
(
)
(
Page 7 of 8
)
COEB223 / MATB324 Formula Sheet
Part 8: Partial Differential Equations Method
Formulation
Elliptic PDEs Liebmann’s Method
Parabolic PDEs (one dimensional)
(
)
Explicit Method (
)
(
Simple Implicit Method (
)
)
(
Crank-Nicolson Method
) (
(
)
Page 8 of 8
)
×
Report "Numerical Methods Formula Sheet"
Your name
Email
Reason
-Select Reason-
Pornographic
Defamatory
Illegal/Unlawful
Spam
Other Terms Of Service Violation
File a copyright complaint
Description
×
Sign In
Email
Password
Remember me
Forgot password?
Sign In
Our partners will collect data and use cookies for ad personalization and measurement.
Learn how we and our ad partner Google, collect and use data
.
Agree & close