Sains Malaysiana 38(2): 227-231(2009)

 

New Parallel R-Point Explicit Block Method For Solving Linear High- Order Ordinary Differential Equations Directly

(Kaedah baru R-titik blok selari tak tersirat bagi menyelesaikan persamaan

pembeza biasa linear peringkat tinggi secara langsung)

 

 

Zurni bin Omar

College of Arts and Sciences, Universiti Utara Malaysia

06010 UUM, Sintok, Kedah, Malaysia

 

Mohamed bin Suleiman

Department of Mathematics, Universiti Putra Malaysia

43400 Serdang, Selangor, Malaysia

 

Received:  23 April 2008 / Accepted:  8 Ogos 2008

 

 

ABSTRACT

 

A new method called parallel R-point explicit block method for solving a single equation of higher order ordinary differential equation directly using a constant step size is developed.  This method calculates the numerical solution at R point simultaneously is parallel in nature.  Computational advantages are presented by comparing the results obtained with the new method with that of the conventional 1-point method.  The numerical results show that the new method reduces the total number of steps and execution time.  The accuracy of the parallel block and the conventional 1-point methods is comparable particularly when finer step sizes are used.

 

Keywords: High-order ordinary differential equations; parallel R-point explicit block method

 

 

ABSTRAK

 

Satu kaedah baru R-titik blok selari tak tersirat bagi menyelesaikan persamaan pembeza biasa peringkat tinggi secara langsung dengan menggunakan  saiz langkah malar dibangunkan. Kaedah selari ini menghitung penyelesaian berangka pada R titik serentak. Kelebihan pengiraan dipersembahkan dengan membandingkan keputusan yang diperolehi daripada kaedah baru dengan kaedah lazim 1-titik. Keputusan berangka menunjukkan kaedah baru mengurangkan jumlah bilangan langkah dan masa pengiraan. Ketepatan kaedah blok selari dan kaedah lazim 1-titik boleh dibandingkan terutamanya bila saiz langkah yang digunakan adalah kecil.

 

Kata kunci:  Kaedah R-titik blok selari tak tersirat; persamaan pembeza biasa peringkat tinggi

 

 

REFERENCES

 

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Suleiman, M.B.  1989.  Solving Higher Order ODEs Directly by the Direct Integration Method. Applied Mathematics and Computation 33(3): 197-219.

 

 

 
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