Advanced Mathematical Methods for Civil Engineering Applications

Advanced Mathematical Methods for Civil Engineering Applications

Ordinary Differential Equations (ODEs) (Section I)(Section I)

Wonsiri Punurai, PhDWonsiri Punurai, PhD

Department of Civil EngineeringRoom 6391, EG Building 3Faculty of Engineering, Mahidol UniversityClass Web: www.egmu.net/~civil/wonsiri

Outline

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Basic ideas - ODEs in Civil Engineering

Basic ideas - ODEs in Civil Engineering

Approximations and Errors Review

Outline

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Use of significant figures

Round-off errors

Approximations and Errors Review

Error Definition

Example – error estimates for iterative methods

See more in later

Example – error estimates for iterative methods

Effect of order of operations

Taylor Series

Outline

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Taylor Series

Taylor series of a function

Taylor series expansions for some common functions

MATLAB example – evaluating the series for sin(x)

Order Notation

Outline

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm

Euler’s Method

Example - Hand Calculation with Euler’s Method

Implementing Euler’s Method in MATLAB

Solving Previous Example using MATLAB