New Nonlinear Four-Step Method for $y''=f(t,y)$

Authors

  • Nazeeruddin Yaacob
  • Chang Phang

DOI:

https://doi.org/10.11113/matematika.v19.n.501

Abstract

Dalam kertas kerja ini, satu kajian telah dijalankan tentang kemungkinan untuk membangunkan satu kaedah empat-langkah taklinear berda\-sarkan min kontraharmonik. Kajian ini telah dijalankan kerana kaedah empat-langkah selalunya memberikan peringkat yang lebih tinggi daripada kaedah terkenal seperti kaedah Numerov dan kaedah Runge-Kutta klasik. Kajian yang terperinci tentang kekonsistenan, kestabilan, penumpuan dan selang berkala telah meyakinkan kita penggunaan kaedah baru ini. Keputusan berangka menunjukkan keputusan yang lebih jitu daripada kaedah yang sedia ada. Katakunci: Min kontraharmonik; selang berkala; masalah nilai awal peringkat kedua. In this paper, a study is made on the possibility of developing a nonlinear four-step method based on contraharmonic mean. The study is done since the four-step methods always give higher order than popular methods like Numerov and classical Runge-Kutta methods. A detailed study of consistency, stability, convergence and interval of periodicity has been done to convince ourselves of using this new method. The numerical results shows that the method is more accurate than the existing one. Keywords: Contraharmonic mean; interval of periodicity; second order initial value problem.

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Published

2003-06-01

Issue

Section

Mathematics