Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations

Yap, Lee Ken (2008) Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations. Masters thesis, Universiti Putra Malaysia.

[img] PDF
678Kb

Abstract

This thesis focuses mainly on deriving block methods of constant step size for solving special second order ODEs. The first part of the thesis is about the construction and derivation of block methods using linear difference operator. The regions of stability for both explicit and implicit block methods are presented. The numerical results of the methods are compared with existing methods. The results suggest a significant improvement in efficiency of the new methods. The second part of the thesis describes the derivation of the r-point block methods based on Newton-Gregory backward interpolation formula. The numerical results of explicit and implicit r-point block methods are presented to illustrate the effectiveness of the methods in terms of total number of steps taken, accuracy and execution time. Both the explicit and implicit methods are more efficient compare to the existing method. The r-point block methods that calculate the solution at r-point simultaneously are suitable for parallel implementation. The parallel codes of the block methods for the solution of large systems of ODEs are developed. Hence the last part of the thesis discusses the parallel execution of the codes. The parallel algorithms are written in C language and implemented on Sun Fire V1280 distributed memory system. The fine-grained strategy is used to divide a computation into smaller parts and assign them to different processors. The performances of the r-point block methods using sequential and parallel codes are compared in terms of the total steps, execution time, speedup and efficiency. The parallel implementation of the new codes produced better speedup as the number of equations increase. The parallel codes gain better speedup and efficiency compared to sequential codes.

Item Type:Thesis (Masters)
Subject:Differential equations
Subject:Differential equations, Linear
Chairman Supervisor:Associate Professor Dr. Fudziah Binti Ismail, PhD
Call Number:FS 2008 18
Faculty or Institute:Faculty of Science
ID Code:5121
Deposited By: Rosmieza Mat Jusoh
Deposited On:06 Apr 2010 02:59
Last Modified:27 May 2013 07:20

Repository Staff Only: Edit item detail


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.