Numerical Analysis Questions & Answers  
Question by Student 201427128
professor, I want to check my solution about A8#3(a).
In Qestion, $\frac{dq}{dt}=-\frac{q}{RC}=f(q_n,t_n)$
Using foward euler method, $q_{n+1}=q_n+\Delta{t}f(q_n,t_n)+O(\Delta{t}^3)$
(given, $q_0=2,RC=3,\Delta{t}=0.2$)
Is it right track? or I have to use $'q=q_0*exp(-\frac{t}{RC})'$ in caculate?
Yes, you're on the right track. You should not be using at all the exact solution.
Question by Jaehyuk
Professor, I have a question about Simpson Rule. When there are even data, we cannot use Simpson Rule, becaue it requires odd data points. In this case, how can we modify the Simpson Rule to integrate.
That was a question asked to you in one assignment problem. I can not give you the answer directly to an assignment question.
Question by Jaehyuk
Professor I have a question about simpson rule. If there are even data, by using $x_{n+\frac{1}{2}}$ we can modify the number of data points into odd number. Is this the right way to use Simpson Rule?
No, you should not change the number of points. The number of points is fixed. You need to find a way to adapt the Simpson rule (or to combine it with another rule) so that it will work on an even number of points.
Question by Student 201427128
professor, I have question about finding L and U. using LU decomposition, I think there are two way to find U. (1)using gaussian elimination. (2)mutiply A by $m_{1,2,...}$like $P_{23}m_1P_{12}A$. I know that using gaussian elimination takes W(operation count) but way(2) is just ($matrix*matrix$). Is it takes W(operation count)?.
In the previous question, you say that multipling with P(partial pivoting) isn't takes W. Does that apply here? I am confused.
Your questions are not clear to me. To find $U$, we do not perform Gaussian elimination. Gaussian elimination is when solving $AX=B$ with $A$ given and without going through $L$ and $U$ matrices.
Question by Student 201427128
Professor, I understand your comment. but I still don't know that Calculate W(operation counting) about $P_{23}m_1P_{12}A$. when I count $P_{23}m_1P_{12}A$,because Partial pivotiong isn't count. Do I just count $m_1A$?
Question by Student 201527119
Professor, I wonder my answer sheet. What time can I see my answer sheet????
You can come on Monday in the afternoon.
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