数值模拟的基本知识-国立中央大学太空科学研究所.pdf

數值模擬的基本知識 by Ling-Hsiao Lyu July 2005 雷射電漿物理暑期學校 Laser-Plasma Interaction Summer School 7/4 ~ 7/9, 2005 中研院原分所浦大邦講堂 數值模擬的基本知識 呂凌霄 國立中央大學 太空科學研究所 1 數值模擬的基本知識 by Ling-Hsiao Lyu July 2005 課程大綱 1. 什麼是數值模擬？ 2. 如何選擇電漿數值模擬碼 3. 處理微分與積分常用的數值方法 4. 處理時間積分的數值方法 5.疊代法與機器誤差估算 6.亂數產生器（補充教材） 7.數值模擬的診斷分析 8. 總結與討論 2 數值模擬的基本知識 by Ling-Hsiao Lyu July 2005 1. 什麼是數值模擬？ Definition of Numerical Simulation Numerical simulations use a set of numerical methods to solve a set of ordinary differential equations and/or partial differential equations, in which at least one time-derivative term is present in these equations. Thus, numerical simulation is a set of carefully planed numerical schemes to solve initial value problems numerically. {Numerical Simulations ⊂ Numerical Methods} Comprehensive knowledge on numerical methods can help us to make a good diagnostics of the simulation results. Objectives of Making Numerical Simulation Studies The goal of using numerical simulations to study nonlinear phenomena includes: To test theoretical model to see if one can reproduce the observed phenomena based on the given theoretical model. To understand detail nonlinear evolution processes and to determine the complicated cause-and-result relationships. To make a prediction or forecast