We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Modified over 4 years ago
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 31 Ordinary Differential Equations
Fig 23.1 FORWARD FINITE DIFFERENCE
Fig 23.2 BACKWARD FINITE DIFFERENCE
Fig 23.3 CENTERED FINITE DIFFERENCE
Data with Errors
Pendulum W=mg Ordinary Differential Equation
ODEs Non Linear Linearization Assume is small
ODEs Second Order Systems of ODEs
Application of ODEs in Engineering Problem SOlving
ODE - OBJECTIVES Undetermined
ODE- Objectives Initial Conditions
ODE-Objectives Given Calculate
Runge-Kutta Methods New Value = Old Value + Slope X Step Size
Runge Kutta Methods Definition of yields different Runge-Kutta Methods
Euler’s Method Let
Sources of Error Truncation: Caused by discretization Local Truncation Propagated Truncation Roundoff: Limited number of significant digits
Sources of Error Propagated Local
Heun’s Method PredictorCorrector 2-Steps
Heun’s Method Predict Predictor-Corrector Solution in 2 steps Let
Heun’s Method Correct Corrector Estimate Let
Error in Heun’s Method
The Mid-Point Method Remember: Definition of yields different Runge-Kutta Methods
Mid-Point Method Predictor Corrector 2-Steps
Mid-Point Method Predictor Predict Let
Mid-Point Method Corrector Correct Estimate Let
Lecture on Numerical Analysis Dr.-Ing. Michael Dumbser
Ordinary Differential Equations
Chapter 6 Differential Equations
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L8&9 KFUPM.
Mechanical Engineering Majors Authors: Autar Kaw, Charlie Barker
PART 7 Ordinary Differential Equations ODEs
Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Ordinary Differential Equations Equations which are.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 6 Roots of Equations Bracketing Methods.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 32 Ordinary Differential Equations.
11 September 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 10 – Ordinary Differential Equations 11 September am – 9.00 am.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 19 Solution of Linear System of Equations - Iterative Methods.
Dr. Jie Zou PHY Chapter 9 Ordinary Differential Equations: Initial-Value Problems Lecture (II) 1 1 Besides the main textbook, also see Ref.: “Applied.
8-1 Chapter 8 Differential Equations An equation that defines a relationship between an unknown function and one or more of its derivatives is referred.
ECIV 301 Programming & Graphics Numerical Methods for Engineers REVIEW III.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 5 Approximations, Errors and The Taylor Series.
Numerical Solutions of Ordinary Differential Equations
NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
CISE301_Topic8L31 SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2,
Differential Equations and Boundary Value Problems
© 2019 SlidePlayer.com Inc. All rights reserved.