Math 104C代做、代写Python、代做c/c++，Java编程设计、代写Gauchospace留学生

日期：2019-04-24 10:48

Math 104C April 26

Midterm

Name:

problem 1

problem 2

problem 3

Total score

Specific Instructions:

1. You are to do this take-home midterm by yourself. You may use your own notes, books, and

libraries, but you should neither consult anyone (including by email) about this exam, nor copy

codes available on line or from anyone else. We repeat: neither collaboration with your classmates

nor copying codes is allowed, and if found, you would be given zero for the midterm.

2. If you find a typo or need a problem clarified, We may occasionally send clarifications or possible corrects via e-mail, so

please check your umail frequently.

3. You must give citations for any material (other than your lecture notes and class handouts)

that you use. Keep in mind that citations are not always correct or sufficient for justification. It

is best to rely on your own reasoning and the material presented in lectures.

4. This midterm will be posted and need to be turned in on Gauchospace with specific deadlines.

The requirements on presenting the answers are the same as your homework. Late midterms will

not be accepted. There is an absolute zero-tolerance policy for late work. Midterms submitted via

email will not be accepted.

1. [10] Do the following questions on convergence rate for nonlinear equations.

(a) Write down the definition for the rate of convergence for iterative methods for solving

nonlinear equations, and use the definition to determine the order of convergence of the

following method to solve x

3 = 5 with the true zero given by x = 51/3

(b) Write a code to implement the above iterative method, and use the obtained numerical

results to verify the convergence rate you get from question (a).

2. [10] Consider the following linear r-step method that solves u

with k as the time step, and t

n = nk. Write down the formula of local truncation error, and

use it to check if the following methods are consistent:

Hint: Using Taylor expansion of two-variables.

3. [10] Choose βj with j = 0, 1, 2 so that the following method has a local truncation error of