Solving First Order Systems of Ordinary Differential Equations Using Parallel R-Point Block Method of Variable Step Size and Order
Zurni B. Omar, and Mohamed Suleiman* Author for corresponding; e-mail address: * zurni@uum.edu.my ** m1suleiman@yahoo.com.my
Volume: Vol.37 No.1 (JANUARY 2010)
Research Article
DOI:
Received: 14 August 2008, Revised: -, Accepted: 25 May 2009, Published: -
Citation: Omar Z.B. and Suleiman M., Solving First Order Systems of Ordinary Differential Equations Using Parallel R-Point Block Method of Variable Step Size and Order, Chiang Mai Journal of Science, 2010; 37(1): 1-13.
Abstract
A new parallel method for solving first order systems of ordinary differential equations using variable step size and order (back value) is developed. The method, known as parallel R-point block method, calculates the numerical solution at more than one point simultaneously.The program of the method employed is run on a shared memory Sequent Symmetry S27 parallel computer. Computational advantages are presented comparing the results obtained by the new method with that of conventional 1-point method. The numerical results show that the new method reduces the total number of steps and execution time. It is also discovered that the accuracy of the parallel r-point block method and the 1-point method is comparable particularly when finer tolerances are used.