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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
