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ENGG 701  Advanced Numerical Methods

ENGG 701 Advanced Numerical Methods   (3-0-3)  
Part of Ph.D. Program, College of Engineering. 

Office Hours :  Any time, please send an e-mail to : ebmattar@uob.edu.bh 
Office No: 14-146-A
Office Location:  College of Engineering, Building 14.
Office Telephone:  ++ 973 17876286,  or  ++ 973 17876606



Department:      All Engineering Departments
Program:            PhD in Engineering
Course code:     ENGG 701  Advanced Numerical Methods
Course credits:  Lecture- Credit Hours 3-0-3
Pre-requisites:    None
Course coordinator:  Prof. Ebrahim A. Mattar


 

ENGG 701 Advanced Numerical Methods   (3-0-3)

This course aims at covering advanced methods of numerical analysis.

It briefs introduction to numerical computing,

approximation and errors which is followed by methods of solving system

of nonlinear equations and approximation of functions.

Numerical solutions of ordinary differential equations;

initial value problems and boundary value problems,

simultaneous differential equations,

Runga-Kutta methods,

finite difference method.

Numerical solution techniques for linear, elliptic, parabolic and hyperbolic partial differential equations.

Methods will be implemented using toolboxes of MATLAB.

Textbook(s):
J.H. Mathews and K. D. Fink, Numerical Methods using Matlab
R. L. Burden and J. D. Faires, Numerical Analysis

 

References:
S. C. Chapra and R. P. Canale, Numerical methods for Engineers
T. J. Akai, Applied Numerical methods for Engineers

 


Course assessment:
Assessment Type Number Weight:


Midterms -1                    30%
Assignments - 5             10%
Projects 1                        20%
Final 1                             40%
Total                              100%



Course Weekly Breakdown:

SOLUTION OF NONLINEAR EQUATIONS
Graphical Method, Bisection Method, Fixed Point Iteration, Aitken’s Acceleration, Steffensen’s Method

SOLUTION OF NONLINEAR EQUATIONS (III)
Roots of Nonlinear Equations, Newton-Raphson Method, Difficulties of Newton-Raphson, Order of Convergence, Secant Method, False Position

SYSTEM OF NON-LINEAR EQUATIONS
Solution of Nonlinear Simultaneous Equations, Substitution Method, Graphical Method, Fixed-Point Iteration, Gauss-Seidel Method

NONLINEAR SYSTEMS OF EQUATIONS (II), Newton Raphson Method

SYSTEM OF LINEAR EQUATIONS:

Roots of Simultaneous Equations, System of Linear Equations,

Direct Methods, (Direct and Iterative Methods), Gaussian Elimination
Partial Pivoting, Scaling, ILL-Conditioning Matrices

LU DECOMPOSITION: LU Factorization, Permutation Matrix, Choleski Decomposition

ITERATIVE METHODS  (I): Iterative Methods, Gauss-Jacobi Method, Gauss-Seidel Method
ITERATIVE METHODS (II): Convergence of Iterative Method
ITERATIVE METHODS (III): Relaxation Method Optimal Relaxation Factor

Interpolation and curve Fitting:  

INTERPOLATION AND POLYNOMIAL APPROXIMATION, Interpolation, Polynomials, Newton Polynomial, Newton Gregory
LAGRANGE APPROXIMATION: Linear Interpolation,  Lagrange Polynomials
CURVE-FITTING:  Curve-Fitting,  Least-SquaresCurve-Fitting,

Non-Polynomials LSCF, Linearization
Numerical Differential and Integration: 

Numerical Solution of Ordinary Differential Equations, Introduction to Finite Difference and Finite Elements

The course  advanced topics related to methods of numerical analysis.

Numerical computing,

Approximation and errors which is followed by methods of solving system

of nonlinear equations and approximation of functions.

Numerical solutions of ordinary differential equations;

initial value problems and boundary value problems,

simultaneous differential equations,

Runga-Kutta methods,

finite difference method.

Numerical solution techniques for linear, elliptic, parabolic and hyperbolic partial differential equations.

Methods will be implemented using toolboxes of MATLAB.

Downloads Area:

Complete  Class Lectures, and Notes Download Here >> ....   Class Notes.    

 

Samples of Course Codes, ...   Useful Examples, 

Graphical Method
Bisection Method
Fixed Point Iteration
Steffensen’s Method

 

ENGG 701_CODING

Download Here >>        ENGG 701_CODING

Extra Notes   Download Here >>        LU-LU_DEComp (from Task),  Norms (1,2, ... inf), Quoted Materials

Lectures Notes: Access via UoB Blackboard link: https://blackboard.uob.edu.bh/ultra/course

Course QAAC Form

The Course also found, over UoB-Blackborad:  https://bb.uob.edu.bh/    or   visit the above LEARNING link
 

Object Oriented Programming using Matlab (OOP):

Object Oriented Programming using Matlab (OOP), uses of classes (class), objects (obj) and data structure (struct) .. if you would like to use this approach in programming for this course, this will be great.  This is optional, but it is always good to learn latest advanced programming tools.  Download slides about Matlab (oop), from the Advanced MATLAB for Scientific Computing, Stanford University.  (press here to download)  OOP-Matlab

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