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。 --

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