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

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 met...

Full description

Saved in:
Bibliographic Details
Main Author: Yap, Lee Ken
Format: Thesis
Language:English
English
Published: 2008
Subjects:
Online Access:http://psasir.upm.edu.my/id/eprint/5121/1/FS_2008_18.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
id my-upm-ir.5121
record_format uketd_dc
spelling my-upm-ir.51212013-05-27T07:20:32Z Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations 2008 Yap, Lee Ken 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. Differential equations Differential equations, Linear 2008 Thesis http://psasir.upm.edu.my/id/eprint/5121/ http://psasir.upm.edu.my/id/eprint/5121/1/FS_2008_18.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations Differential equations, Linear Science English
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
English
topic Differential equations
Differential equations

spellingShingle Differential equations
Differential equations

Yap, Lee Ken
Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations
description 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.
format Thesis
qualification_level Master's degree
author Yap, Lee Ken
author_facet Yap, Lee Ken
author_sort Yap, Lee Ken
title Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations
title_short Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations
title_full Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations
title_fullStr Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations
title_full_unstemmed Direct Block Methods for Solving Special Second Order Ordinary Differential Equations and Their Parallel Implementations
title_sort direct block methods for solving special second order ordinary differential equations and their parallel implementations
granting_institution Universiti Putra Malaysia
granting_department Science
publishDate 2008
url http://psasir.upm.edu.my/id/eprint/5121/1/FS_2008_18.pdf
_version_ 1747810355453624320