ME 581 Numerical Methods No.2
Zhicheng Zhang
October 16, 2011
Part. 1
Problem.2.1.1 Verify that the equation ln(1 + x) cos(x) = 0 has a root
on the interval (0, 1). Next, Perform the bisection method
ME 575
HOMEWORK 1
Due September 12, 2017
Please start all problem solutions on a new sheet of paper and box any final results. Submit by the
beginning of the class period on the due date.
1.
A system
Problem 1
The function = ! 2 ! + 2 1 is plotted below. The function has a root at
= 1.
(a) Find an approximation of the root by performing four iterations of Newtons
ME581 Homework 1
Due: September 15, 2016
Your computer programs should be uploaded using SVN, the file should be named as requested for each problem.
Hand calculation problems and the results of your
ME581 Homework 2
Due: September 29, 2016
Your computer program should be uploaded using SVN. The file should be named
lastname_hw2.X .
Hand calculations and the results of your computer codes should b
ME 581
Homework 5
(Due: Thursday, November 10, 2016)
Problems 6 and 7 are to be solved by a computer program that you have written, upload
the code using SVN
Problem 1
Evaluate numerically
2
(3 x
2 5
Homework 3
ME 581
Due October 13 2016
For all the problems you need to write/print your solutions and plots and return
them as a single hard copy.
The codes are submitted using SVN.
For each pr
ME 581 Homework 2 Solutions
Problem 1
(i)
(ii)
Error:
Residual:
= [2 1]
= [0 0.002]
(iii)
Relative Error:
(iv)
Condition Number :
(v)
Relative Residual:
(vi)
Product of the Condition Number and the
ME8281 - Last updated: April 21, 2008
(c) Perry Li
Robust stability and Performance
Topics: ([ author ] is supplementary source)
Sensitivities and internal stability (Goodwin 5.1-5.4)
Modeling Error
Homework 4
ME 581
Due October 27, 2016
This homework does not require written code.
Lagrange Interpolation
Problem 1:
Let = 3, 1 = 0, 2 = 2, and 3 = .
(a) Determine formulas for the Lagrange polynomia
ME581 Homework 1
Due: 4:15pm September 12, 2017
The following problems are to be documented, solved, and presented in a Jupyter notebook.
On-Campus students: Save the notebook as a single PDF, then pr
Prob. 4
cfw_
0.6661
0.4022
(1) Partial pivoting x=
1.0801
0.3590
with four decimal digits.
(2) The same as given by (1) with four decimal digits. The actual difference between the two
answers are usi
Last class
Today
1. Scientific computing
2. Sources of error
3. Review systems of
linear equations
1. Nonlinear equations:
1. Existence and
uniqueness.
2. Convergence rates.
2.
3.
4.
5.
HWI
Interval
Last class
Today
1. Scientific computing
2. Sources of error
3. Review systems of
linear equations
1. Nonlinear equations:
1. Existence and
uniqueness.
2. Convergence rates.
2.
3.
4.
5.
Interval bise
Last class
Today
1. Differentiation
1. Ordinary differential
equations
1. Read: Chapter 7
ODE
y'(t) = f (t, y(t)
y(0) = A
Example
For t>0
Unstable
y=y
Eulers method
Example
y=y,
Last class
Today
1. Scientific computing
2. Sources of error
1. rounding error
2. truncation error
3. sensitivity and
conditioning
4. cancellation
3. Systems of Linear
Equations
1. Notation
2. Existe
Last class
Today
1. Scientific computing
2. Sources of error
3. Review systems of
linear equations
1. Nonlinear equations:
1. Existence and
uniqueness.
2. Convergence rates.
2.
3.
4.
5.
Interval bisec
Last class
Today
1. Scientific computing
2. Sources of error
3. Review systems of
linear equations
1. Nonlinear equations:
1. Existence and
uniqueness.
2. Convergence rates.
2.
3.
4.
5.
Interval bise
Last class
Today
1. Scientific computing
2. Sources of error
1. rounding error
2. truncation error
3. sensitivity and
conditioning
4. cancellation
3. Systems of Linear
Equations
1. Notation
2. Existen
Last class
Today
1. Nonlinear equations:
1.
2.
3.
4.
1. Existence and
uniqueness.
2. Convergence rates.
2. Interval bisection
Fixed point
Newtons method
Secant method
Systems of non-linear
equations
Problem 1
Consider the linear system:
1.8260 x1 +1.3185 x2 = 0.5075
0.2285 x1 + 0.1653 x2 = 0.0632
a) Use four-digit decimal in every arithmetic operation with Gaussian elimination (withou