'Truncation error' presentation slideshows

Ordinary Differential Equations

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Numerical Solutions of Ordinary Differential Equations

CHAPTER 6. Numerical Solutions of Ordinary Differential Equations. Contents. 6.1 Euler Methods and Error Analysis 6.2 Runge-Kutta Methods 6.3 Multistep Methods 6.4 Higher-Order Equations and Systems 6.5 Second-Order Boundary-Value Problems. 6.1 Euler Method and Error Analysis.

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Chapter 4.3 Real-time Game Physics

Chapter 4.3 Real-time Game Physics. Outline. Introduction Motivation for including physics in games Practical development team decisions Particle Physics Particle Kinematics Closed-form Equations of Motion Numerical Simulation Finite Difference Methods Explicit Euler Integration

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Numerical Integration Techniques

Numerical Integration Techniques. A Brief Introduction By Kai Zhao January, 2011. Objectives. Start Writing your OWN Programs Make Numerical Integration accurate Make Numerical Integration fast CUDA acceleration. The same Objective. Lord, make me accurate and fast.

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Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations. CAAM 452 Spring 2005 Lecture 9 Instructor: Tim Warburton. Today. Introduction to a very basic finite volume method. Mass Conservation.

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Numerical Methods in Computational Fluid Dynamics (CFD)

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Numerical Methods in Computational Fluid Dynamics (CFD)

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John Arrington, Argonne National Laboratory ECT* Workshop on the Proton Radius Puzzle

Extracting the proton charge and magnetization radii from low-Q 2 polarized/unpolarized electron/muon scattering. Graphic by Joshua Rubin, ANL. John Arrington, Argonne National Laboratory ECT* Workshop on the Proton Radius Puzzle. Outline. JLab form factor measurements

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MA5233: Computational Mathematics

MA5233: Computational Mathematics Weizhu Bao Department of Mathematics & Center for Computational Science and Engineering National University of Singapore Email: bao@math.nus.edu.sg URL: http://www.math.nus.edu.sg/~bao Computational Science Third paradigm for Discovery in Science

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OVERVIEW

OVERVIEW. MULTIGRID. Why multigrid? Basic multigrid principles Full multigrid (FMG) Nonlinear multigrid (FAS) Adaptive multigrid. Why Multigrid?. Error Components.

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Lecture 4 - Numerical Errors

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Sources of Error

Sources of Error. Major: All Engineering Majors Authors: Autar Kaw, Luke Snyder http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Sources of Error http://numericalmethods.eng.usf.edu. Two sources of numerical error. Round off error

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MA557/MA578/CS557 Lecture 5a

MA557/MA578/CS557 Lecture 5a. Spring 2003 Prof. Tim Warburton timwar@math.unm.edu. Homework 2 correction. Q4) Implement the numerical approximation of: By:. Homework 2 cont. Q4 cont) For N=10,40,160,320,640,1280 run to t=10 , with: dx = (8/(N-1))

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MA557/MA578/CS557 Lecture 5

MA557/MA578/CS557 Lecture 5. Spring 2003 Prof. Tim Warburton timwar@math.unm.edu. Homework 2 correction. Q4) Implement the numerical approximation of: By:. Homework 2 cont. Q4 cont) For N=10,40,160,320,640,1280 run to t=10 , with: dx = (8/(N-1))

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Chapter 4

Chapter 4. Truncation Errors and the Taylor Series. n th order approximation. (x i+1 -x i )= h step size (define first). Reminder term, R n , accounts for all terms from (n+1) to infinity. Fig 4.1. e is not known exactly, lies somewhere between x i+1 > e >x i .

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1.3. Sources of Error

1.3. Sources of Error. Two sources of numerical error. Round off error Truncation error. Round-off Error. Round off Error. Caused by representing a number approximately. Truncation Error. Truncation error. Error caused by truncating or approximating a mathematical procedure.

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Chapter 3- Model Fitting

Chapter 3- Model Fitting. Three T asks W hen A nalyzing D ata:. Fit a model type to the data. Choose the most appropriate model from the ones that have been fitted. Make predictions based on the data. Project Outline:.

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Chapter 9

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