Nazeeruddin Yaacob

A Fifth -Order Five-Stage RK-Method Based on Harmonic Mean

In this paper a fifth-order five-stage Runge-Kutta formula based on Harmonic mean is developed for solving initial value problem of the type y′ = f(y), y(x 0) = y 0. The stability analysis reveals that the region of absolute stability for this method is larger than that of Taylor series’s method of order five. Numerical examples indicate that this method is superior when compared to some existing methods including the 5-stage GM-RK method, Taylor Series’s method of order 5, and RK5(6) method of Nystrom version.

Penganggaran dan Pengawalan Ralat Dalam Kaedah HaM-4(4) Untuk Penyelesaian Masalah Nilai Awal

Dalam kertas ini satu kaedah baru yang berasaskan gabungan min harmoni dan min aritmatik berperingkat keempat dirumuskan. Kaedah ini, beserta kaedah Rungge-Kutta-Harmoni, RK-HaM dapat mambantu menganggarkan ralat dalam penyelesaian masalah nilai awal. Rantau kestabilan mutlak untuk kaedah ini juga dikaji. Contoh penyelesaian berangka yang dikemukakan menunjukkan keberkesanan kaedah ini. Katakunci: Kaedah RK-HaM; kaedah RK-AHM; Kaedah HaM-RK4(4); kestabilan anggaran ralat; pengawal ralat In this papaer a new fourth order formula based on harmonic and arithmatic means is formulated. The formula when used with the Harmonic-Rungge-Kutta formula is capable of estimating the local truncution error in solving initial value problems. The absolute stability region of the method is also studied. The numerical results presented showed the effectiveness of the method. Keywords: RK-HaM method; RK-AHM method; HaM-RK4(4) method; stability; error estimate; error control