Sains Malaysiana 29: 93-102 (2000)                                                                                      Pengajian Kuantitatif /

Quantitative Studies

A New High Order Iterative Alternating Decomposition Explicit

Method to Solve the Heat Conduction Equation

M.S. Sahimi, E. Subdararajan, M. Subramaniam & N.A.A. Hamid

Department of Engineering Sciences and Mathematics

Universiti Tenaga Nasional

43009 Kajang, Selangor D.E., Malaysia

ABSTRACT

In this paper, a new iterative alternating decomposition explicit (lADE) scheme of order of accuracy similar to that of Sahimi et al. (1993) of the Mitchell-Fairweather variant is developed to solve the one-dimensional parabolic problem. It is based on the two-stage fractional splitting strategy suggested by D'Yakonov and our numerical experiments indicate that the method is more accurate than the recently developed Alternating Group Explicit (AGE) method of Peaceman-Rachford variant.

ABSTRAK

Dalam makalah ini, skema tak tersirat penghuraian berselang-seli secara lelaran (TTHSL) yang baru yang mempunyai peringkat kejituan yang sama seperti yang diperoleh Sahimi et al. (1993) dibina untuk menyelesaikan masalah parabolik satu matra. Skema ini diasaskan kepada strategi pembelahan pecahan dua tahap yang dicadangkan oleh D'Yakonov dan uji kaji berangka kami mendapati kaedah tersebut lebih jitu daripada kaedah tak tersirat kumpulan selang-seli yang diperoleh daripada varian Peaceman­-Rachford.

REFERENCES/RUJUKAN

D'Yakonov, Ye G. 1963. On the application of disintegrating difference operators. Z. Vycisl. Mat. i. Mat. Fiz. 3: 385-388.

Evans, D.J., & Sahimi, M.S. 1989. The alternating group explicit iterative method (AGE) to solve parabolic and hyperbolic partial differential equations. In Tien, E.L. & Chawla, T.E. (Eds.). Ann. Rev. Num. Fluid Mech. and Heat Trans. 2: 283-389. New York: Hemisphere Publication Corporation.

Johnson, L.W. & Riess, R.D. 1982. Numerical analysis. 2nd Ed. Reading: Addison­ Wesley Publication Company.

Lapidus, L. & Pinder, G.F. 1982. Numerical solution of partial differential equations in science and engineering. New York: John Wiley and Sons.

Mitchell, A.R. & Griffiths, D.F. 1980. The finite difference method in partial differential equations. Chichester: John Wiley and Sons.

Sahimi, M.S., Ahmad, A., & Bakar, A.A. 1993. The iterative alternating decomposi­tion explicit method (lADE) method to solve the heat conduction equation. Intern. J. Computer Math. 46: 219-229

Saulev, V.K. 1964. Integration of equations of parabolic type by the method of nets. Oxford: Pergamon Press.

Subramaniam, M. 1999. Kaedah tak tersirat penghuraian berselang-seli secara lelaran menggunakan varian D'Yakonov bagi menyelesaikan persamaan parabolik. SmSn thesis. Universiti Kebangsaan Malaysia.