Sains Malaysiana 45(6)(2016): 1007–1012

Quintic Spline Method for Solving Linear and Nonlinear Boundary Value Problems

(Kaedah Splin Kuintik untuk Menyelesaikan Masalah Nilai Sempadan Linear dan Tak Linear)

OSAMA ALA'YED*, TEH YUAN YING & AZIZAN SAABAN

School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia

Diserahkan: 15 Januari 2015/Diterima: 27 Ogos 2015

ABSTRACT

In this article, a fourth order quintic spline method has been developed to obtain numerical solutions for second order boundary value problems with Dirichlet boundary conditions. The developments of the quintic spline method and convergence analysis were presented. Three test problems have been considered for comparison purposes. The numerical results showed that the quintic spline method is more accurate compared to existing cubic spline method when solving nonlinear second order boundary value problems but vice versa when solving linear second order boundary value problems.

Keywords: Boundary value problem; quintic spline method; shooting method; spline interpolation

ABSTRAK

Dalam artikel ini, satu kaedah splin kuintik peringkat keempat telah dibangunkan untuk memperoleh penyelesaian berangka bagi masalah nilai sempadan peringkat kedua dengan syarat sempadan Dirichlet. Pembangunan kaedah splin kuintik dan analisis penumpuan telah dibentangkan. Tiga masalah ujian telah diambil kira untuk tujuan perbandingan. Keputusan berangka menunjukkan bahawa kaedah splin kuintik adalah lebih tepat berbanding dengan kaedah splin kubik sedia ada apabila menyelesaikan masalah nilai sempadan tak linear peringkat kedua, tetapi sebaliknya apabila menyelesaikan masalah nilai sempadan linear peringkat kedua.

Kata-kata kunci: Interpolasi splin; kaedah splin kuintik; kaedah tembakan; masalah nilai sempadan

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