Universiti Teknologi Malaysia Institutional Repository

Verification of boundary integral equation for conformal mapping of doubly connected regions onto a disk with a slit

Lai, Tze Wee (2010) Verification of boundary integral equation for conformal mapping of doubly connected regions onto a disk with a slit. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.

[img]
Preview
PDF
34Kb
[img]
Preview
PDF
83Kb
[img]
Preview
PDF
72Kb

Abstract

In this study, we discussed a new Fredholm integral equation of the second kind with classical Neumann kernel associated to ????, where ? is a conformal mapping of bounded multiply connected regions onto a disk with slit domain. The boundary integral equation is constructed from a boundary relationship satisfied by a function that is analytic on a multiply connected region. The boundary integral equation is linear and does not contain any unknown radii. For numerical verification, we parameterized and discretized the integral equation by using the Nyström’s method with trapezoidal rule. Five test bounded doubly connected regions are chosen to verify the new boundary integral equation using the exact mapping functions. The five test regions are annulus, circular frame, frame of Limacon, elliptic frame and frame of Cassini’s oval.

Item Type:Thesis (Masters)
Additional Information:Thesis (Sarjana Sains (Matematik Kejuruteraan)) - Universiti Teknologi Malaysia, 2010; Supervisor : Assoc. Prof. Dr. Ali Hassan Mohamed Murid
Uncontrolled Keywords:Fredholm integral equation, Neumann kernel, boundary integral equation
Subjects:Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions:Science
ID Code:19163
Deposited By: Kamariah Mohamed Jong
Deposited On:01 Feb 2012 01:47
Last Modified:01 Feb 2012 01:54

Repository Staff Only: item control page