By Kankesu Jayanthakumaran (Editor)
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Extra info for Advanced Technologies
46 Advanced Technologies Parallel direct integration variable step block method for solving large system of higher order ordinary differential equations 47 X3 Parallel direct integration variable step block method for solving large system of higher order ordinary differential equations Zanariah Abdul Majid and Mohamed Suleiman Universiti Putra Malaysia Malaysia 1. Introduction The performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs) has been investigated.
95 speed up and 98% efficiency for the two processors. 2. Background The ever-increasing advancement in computer technology has enabled many in science and engineering sectors to apply numerical methods to solve mathematical model that involve ODEs. The numerical solution of large ODEs systems requires a large amount of computing power. Users of parallel computing tend to be those with large mathematical problems to solve with the desire to obtain faster and more accurate results. In this paper, we consider solving directly the higher order IVPs for system of ODEs of the form (1) y ′′ = f (x, y, y ′) , y (a ) = y 0 , y′(a ) = y0′ , x ∈ [a, b] .
In Table 1 – 5 show the numerical results for the tested problems. For sequential S2PFDIR only one processor was used and two processors were employed for the parallel algorithms of P2PFDIR. The numerical results show that the parallel execution time is faster than the sequential execution time for large ODEs systems. In Table 1 – 3, without loss of generality, we only compute the MAXE at TOL = 10 −2 since the execution time is grossly increased with a finer tolerance. 682821 Table 1. Numerical results of 2PFDIR Method for Solving Problem 1 When N=1000.
Advanced Technologies by Kankesu Jayanthakumaran (Editor)