课程名称︰数值分析 课程性质︰机械系大学部/研究所选修 课程教师︰黄美娇 开课学院：工学院 开课系所︰机械工程学系 考试日期（年月日）︰2011.06.21 考试时限（分钟）：60 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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 注：前三题必须使用「中文」回答，繁体字简体字皆可接受。 --

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