課程名稱︰數值分析
課程性質︰機械系大學部/研究所選修
課程教師︰黃美嬌
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰2011.06.21
考試時限（分鐘）：60
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Problem1：(20%)
What is the so-called "truncation error"? Consider a finite difference
formula for a derivative of a function f(x). How does the accuracy vary the
increment Δx? Why so?
Problem2：(20%)
What is so-called "numerical diffusion"? What effect does it cause if
it is positive? What may happen if it is negative?
Problem3：(20%)
Given an initial-valued problem, if a multi-step time marching scheme
is desired, describe what you can do in order to obtain the solution at early
times before the multi-step scheme can be applied.
Problem4：(40%)
N
Consider a set of evenly spaced nodes {x } . We are interested in
i i=0
approximating f"(x1) ≒ a0f_0 + a1f_1 + a2f_2 + a3f_3 + a4f_4 , where
f_i = f(x ). Find the system of algebraic equations for the coefficients
i
a 's and the order of the accuracy of this finite-difference formula.
i
註：前三題必須使用「中文」回答，繁體字簡體字皆可接受。
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.44.41