Applied and Computational Complex Analysis Seminar Series

APPLIED AND COMPUTATIONAL COMPLEX ANALYSIS SEMINAR SERIES (Part 1) SEMESTER I, 2010/2011

Date/Day : Wednesday, 28 July 2010 (Week 3) Time : 8:30 am – 1:00 pm Venue : Seminar Room 1, Ibnu Sina Institute, UTM Skudai Chairperson : Assoc. Prof. Dr. Ali Hassan Mohamed Murid

Time Speakers

Chye Mei Sian, M.Sc. Student 9:00 – 9:30 am “A Boundary Integral Equation for the Exterior Neumann Problem on Multiply Connected Region”

Arif Asraf Mohd Yunos, PhD Student 9:30 – 10:00 am “Boundary Layer Flow along the Vertical Wall”

10:00 – 10.30 am Tea/Coffee Break

Ali Wahab Kareem Sangawi, PhD Student 10:30 – 11.00 am “Integral and Differential Equations for Conformal Mapping of Bounded Multiply Connected Regions onto a Circular Slit Region”

Samer Al-Hetemi, PhD Student 11:00 – 11:30 pm “To be announced”

Organized by

Applied Algebra and Analysis Group (A3G), Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, Skudai, Johor www.ibnusina.utm.my/AAAG

Limited to 20 participants. Please contact Assoc. Prof. Dr. Ali Hassan Mohamed Murid for reservation and further details. Tel: 07-5536072, 07-5534245 or 012-7207253. E-mail : [email protected] or [email protected]. Fax: 07-5536080 ABSTRACTS ______

A Boundary Integral Equation for the Exterior Neumann Problem on Multiply Connected Region

Chye Mei Sian Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Skudai, Johor [email protected]

Supervisor:

Assoc Prof Dr Ali Hassan Mohamed Murid Ibnu Sina Institute for Fundamental Science Studies, UTM Skudai, Johor

Abstract

This talk will discuss some results contained in the following papers:

A. Jumandi, E.M.A. Alejaily, A.H.M. Murid & H. Rahmat, Computing the Solution of the Neumann Problem Using Integral Equation and Runge-Kutta Method, Proceedings of Regional Annual Fundamental Science Seminar 2010.

M.M.S. Nasser, A.H.M. Murid, M. Ismail and E.M.A. Alejaily, Boundary Integral Equations with the Generalized Neumann Kernel for Laplace’s Equation in Multiply Connected Regions. (submitted to international journal for publication)

Keywords. Neumann problem; Riemann-Hilbert problem; Integral Equation; Generalized Neumann Kernel. BOUNDARY LAYER FLOW ALONG THE VERTICAL WALL

Arif Asraf Mohd Yuns Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Skudai, Johor [email protected]

Supervisor:

Assoc Prof Dr Ali Hassan Mohamed Murid Ibnu Sina Institute for Fundamental Science Studies, UTM Skudai, Johor

Abstract

This talk is related to my undergraduate project under the supervision of Dr. Maslan Osman. In investigating the boundary layer flow along a vertical wall, a mathematical formulation has been formulated using similarity transformation. Three governing equation which are continuity equation, momentum equation and energy equation had been derived using Reynolds transport theorem. Since the Reynolds transport theorem will give the governing equation in integral form, the equation obtained from Reynolds transport theorem need to be changed to differential form using fluid terminologies and calculus vector identity. Then this governing equation has been transformed from partial differential equation to ordinary differential form . In order to solve numerically, Fortran Force software was used to obtain the result. By using Matlab, graph for velocity profile and temperature profile have been plotted and the analyzed.

Keywords. Boundary layer flow; Reynolds transport theorem; Calculus Vector; Keller Box method Integral and Differential Equations for Conformal Mapping of Bounded Multiply Connected Regions onto a Circular Slit Region

ALI WAHAB KAREEM Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Skudai, Johor Ibnu Sina Institute for Fundamental Science Studies, UTM Skudai, Johor

[email protected]

Supervisor:

Assoc Prof Dr Ali Hassan Mohamed Murid Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 81310 UTM Skudai, Johor

Abstract

Conformal mapping is an important and useful tool in science and engineering. However exact mapping functions are unknown except for some special regions. This talk will present a new boundary integral equation with classical Neumann kernel associated to f  f , where f is a conformal mapping of bounded multiply connected regions onto the circular slit region. This boundary integral equation is constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. With f  f known one can then treat it as a differential equation for computing f .

Keywords. Conformal mapping; Boundary integral equations; Neumann kernel; Differential equations