Sains Malaysiana
39(6)(2010): 1049–1054
Embedded Pair of
Diagonally Implicit Runge-Kutta Method for Solving Ordinary Differential Equations
(Pasangan
Terbenam Kaedah Runge-Kutta Pepenjuru Tersirat untuk Menyelesaikan Persamaan Pembezaan)
Fudziah Ismail*, Raed Ali Al-Khasawneh, Mohamed Suleiman & Malik Abu Hassan
Jabatan Matematik, Fakulti
Sains, Universiti Putra Malaysia , 43400 UPM Serdang
Selangor, Malaysia
Diserahkan: 9 April 2009 /
Diterima: 26 Jun 2009
ABSTRACT
Improvements
over embedded diagonally implicit Runge-Kutta pair of order four in five are
presented. Method of higher stage order with a zero first row and the last row
of the coefficient matrix is identical to the vector output is given. The
stability aspect of it is also looked into and a standard test problems are
solved using the method. Numerical results are tabulated and compared with the
existing method.
Keywords:
Diagonally implicit; Runge-Kutta; stiff equations; stability
ABSTRAK
Penambahbaikan
pasangan terbenam kaedah Runge-Kutta pepenjuru tersirat dipersembahkan. Kaedah
dengan peringkat tahap yang lebih tinggi dengan baris pertama sifar dan baris
terakhir matriks pekali sama dengan vektor output diberikan. Aspek
kestabilannya dikaji dan beberapa masalah piawai diselesaikan menggunakan
kaedah tersebut. Keputusan berangka diberikan dan dibandingkan dengan kaedah
sedia ada.
Kata
kunci: Kestabilan; Pepenjuru tersirat; persamaan kaku; Runge-Kutta
RUJUKAN
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*Pengarang untuk surat-menyurat; email: fudziah@math.upm.edu.my
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