Numerical Evaluation of Cauchy Type Singular Integrals Using Modification of Discrete Vortex Method

Mahiub, Mohammad Abdulkawi (2007) Numerical Evaluation of Cauchy Type Singular Integrals Using Modification of Discrete Vortex Method. Masters thesis, Universiti Putra Malaysia.

[img] PDF
542Kb

Abstract

In this thesis, characteristic singular integral equations of Cauchy type ()(),LtdtfxxLxtϕ=∈−∫ (1) where L is open or closed contour, are examined. The analytical solutions for equation (1) are described. Some examples of solution for certain functions f (x) are given. A quadrature formula for evaluation of Cauchy type singular integral (SI) of the form 11(),11tdtxxtϕ−−<<−∫ (2) is constructed with equal partitions of the interval [−1,1] using modification discrete vortex method (MMDV), where the singular point x is considered in the middle of one of the intervals [tj, tj+1], j=1,…, n. It is known that the bounded solution of equation (1) when L=[−1,1] is 12211,111ftxxdtttxϕπ−−=−−∫ (3) A quadrature formula is constructed to approximate the SI in (3) using MMDV and linear spline interpolation functions, where the singular point x is assumed to be at any point in the one of the intervals [tj,tj+1], j=1,…, n. The estimation of errors of constructed quadrature formula are obtained in the classes of functions C1[−1,1] and Hα(A,[−1,1]) for SI (2) and Hα(A,[−1,1]) for (3). For SI (2), the rate of convergence is improved in the class C1[−1,1], whereas in the class Hα(A,[−1,1]), the rate of convergence of quadrature formula is the same of that of discrete vortex method (MDV). FORTRAN code is developed to obtain numerical results and they are presented and compared with MDV for different functions f(t). Numerical experiments assert the theoretical results.

Item Type:Thesis (Masters)
Subject:Cauchy integrals
Subject:Numerical analysis
Chairman Supervisor:Nik Mohd Asri Nik Long, PhD
Call Number:FS 2007 30
Faculty or Institute:Faculty of Science
ID Code:5021
Deposited By: Rosmieza Mat Jusoh
Deposited On:02 Apr 2010 08:46
Last Modified:27 May 2013 07:19

Repository Staff Only: Edit item detail

Document Download Statistics

This item has been downloaded for since 02 Apr 2010 08:46.

View statistics for "Numerical Evaluation of Cauchy Type Singular Integrals Using Modification of Discrete Vortex Method"


Universiti Putra Malaysia Institutional Repository

Universiti Putra Malaysia Institutional Repository is an on-line digital archive that serves as a central collection and storage of scientific information and research at the Universiti Putra Malaysia.

Currently, the collections deposited in the IR consists of Master and PhD theses, Master and PhD Project Report, Journal Articles, Journal Bulletins, Conference Papers, UPM News, Newspaper Cuttings, Patents and Inaugural Lectures.

As the policy of the university does not permit users to view thesis in full text, access is only given to the first 24 pages only.