Sains Malaysiana 40(11)(2011): 1285–1290

Extended Cubic B-spline Method for Linear Two-Point

Boundary Value Problems

(Kaedah Splin-B Kubik Lanjutan untuk Masalah Nilai Sempadan Dua Titik Linear)

Nur Nadiah Abd Hamid*, Ahmad Abd. Majid & Ahmad Izani Md. Ismail

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang

Malaysia

Received: 20 September 2010 / Accepted: 30 March 2011

ABSTRACT

Second order linear two-point boundary value problems were solved using extended cubic B-spline interpolation method. Extended cubic B-spline is an extension of cubic B-spline consisting of one shape parameter, called λ. The resulting approximated analytical solution for the problems would be a function of λ. Optimization of λ was carried out to find the best value of λ that generates the closest fit to the differential equations in the problems. This method approximated the solutions for the problems much more accurately compared to finite difference, finite element, finite volume and cubic B-spline interpolation methods.

Keyword: Cubic B-spline; extended cubic B-spline; spline interpolation; two-point boundary value problem

ABSTRAK

Masalah nilai sempadan dua titik linear peringkat kedua diselesaikan menggunakan kaedah interpolasi Splin-B kubik lanjutan. Splin-B kubik lanjutan ialah satu perlanjutan daripada Splin-B kubik yang mengandungi satu parameter bentuk, iaitu λ. Penyelesaian analitikal anggaran yang terhasil kepada masalah tersebut merupakan fungsi λ. Pengoptimuman λ dijalankan untuk mencari nilai λ yang terbaik yang menghasilkan penyesuaian terdekat kepada persamaan pembezaan dalam masalah tersebut. Kaedah ini menganggarkan penyelesaian untuk masalah tersebut dengan lebih tepat berbanding dengan kaedah-kaedah beza terhingga, unsur terhingga, isipadu terhingga dan interpolasi Splin-B kubik.

Kata kunci: Interpolasi splin; masalah nilai sempadan dua titik; Splin-B kubik; Splin-B kubik lanjutan

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*Corresponding author; email: nurnadiah_abdhamid@yahoo.com