Sains Ma1aysiana 25(4) 1996: 1-10                                                    Pengajian Kuantitatif/

                                                                                                             Quantitative Studies

Hubungan di antara Jejari Spektrum dan Faktor Pengenduran

Berlebihan untuk Masalah Nilai Sempadan Berkala

dalam Persamaan Pembeza Separa Eliptik

(Relationship between spectral radius and overrelaxation factor for a periodic boundary value problem in the second-order linear self-adjoint ellliptic partial differential equation)

Mohd Idris Jayes

Jabatan Statistik

Fakulti Sains Matematik

Universiti Kebangsaan Malaysia

43600 UKM Bangi Selangor D.E.

ABSTRACT

The discretization of the second-order linear self-adjoint ellliptic partial differential equation problem subject to periodic boundary conditions results in a system of linear equations of the form Mu = s, where M is a block cyclic tridiagonal square matric. In this paper, the relationship between the spectral radius and overrelaxation factor for the problem is derived.

ABSTRAK

Pendiskretan masalah persamaan pembeza separa (PPS) eliptik swadampingan linear peringkat kedua menghasilkan satu sistem persamaan linear bentuk Mu = s, dengan M merupakan satu matriks segiempatsama tiga pepenjuru berkitar blok. Dalam kertas ini, hubungan di antara jejari spektrum dan faktor pengenduran berlebihan untuk masalah itu akan dirumuskan.

RUJUKAN/REFERENCES

Anns, R.J., Gates, L.D., & Zondek, B. 1956. A method of block iteration, J. Soc. Ind. Appl. Maths., 4: 220-229.

Mohd Idris Jayes. 1992. Numerical solution of ordinary and partial differential equations occurring in scientific applications, Ph.D. Thesis, Loughborough University of Technology, U.K.

Young, D.M. 1971. Iterative solution of large systems, New York: Academic Press.