Penyelesaian terus persamaan pembezaan biasa peringkat tiga menggunakan kaedah blok hibrid kolokasi diperbaiki

Translated title of the contribution: Solution of third order ordinary differential equation using improved block hybrid collocation method

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The improved block hybrid collocation method (KBHK(B)) with two off-step points and four collocation points is proposed for the direct solution of general third order ordinary differential equations. Modification is done by adding first derivative of third order function into the general form of block hybrid collocation method to yield KBHK(B). Both main and additional methods are derived via interpolation (power series function) and collocation of the basic polynomial. An improved block method is derived to provide the approximation at five points concurrently. Zero stability, consistency, convergence and absolute stability region of KBHK(B) are investigated. Some numerical examples with exact solution are tested to illustrate the efficiency of the method. KBHK(B) is compared by other block hibrid collocation method in term of global error and step number. It is shown that KBHK(B) generates minimum global error with minimum step number.

Original languageMalay
Pages (from-to)2179-2186
Number of pages8
JournalSains Malaysiana
Volume47
Issue number9
DOIs
Publication statusPublished - 1 Jan 2018

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Third Order Differential Equation
Hybrid Method
Collocation Method
Ordinary differential equation
Block Method
Collocation
Absolute Stability
Stability Region
Global Minimum
Power series
Exact Solution
Interpolate
Derivative
Numerical Examples
Polynomial
Zero
Term
Approximation

ASJC Scopus subject areas

  • General

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Penyelesaian terus persamaan pembezaan biasa peringkat tiga menggunakan kaedah blok hibrid kolokasi diperbaiki. / Chien, Lee Khai; Din, Ummul Khair Salma; Ahmad, Rokiah @ Rozita.

In: Sains Malaysiana, Vol. 47, No. 9, 01.01.2018, p. 2179-2186.

Research output: Contribution to journalArticle

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abstract = "The improved block hybrid collocation method (KBHK(B)) with two off-step points and four collocation points is proposed for the direct solution of general third order ordinary differential equations. Modification is done by adding first derivative of third order function into the general form of block hybrid collocation method to yield KBHK(B). Both main and additional methods are derived via interpolation (power series function) and collocation of the basic polynomial. An improved block method is derived to provide the approximation at five points concurrently. Zero stability, consistency, convergence and absolute stability region of KBHK(B) are investigated. Some numerical examples with exact solution are tested to illustrate the efficiency of the method. KBHK(B) is compared by other block hibrid collocation method in term of global error and step number. It is shown that KBHK(B) generates minimum global error with minimum step number.",
keywords = "Block hibrid collocation method, Consistency, Convergence, Third order ordinary differential equations, Zero stability",
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AB - The improved block hybrid collocation method (KBHK(B)) with two off-step points and four collocation points is proposed for the direct solution of general third order ordinary differential equations. Modification is done by adding first derivative of third order function into the general form of block hybrid collocation method to yield KBHK(B). Both main and additional methods are derived via interpolation (power series function) and collocation of the basic polynomial. An improved block method is derived to provide the approximation at five points concurrently. Zero stability, consistency, convergence and absolute stability region of KBHK(B) are investigated. Some numerical examples with exact solution are tested to illustrate the efficiency of the method. KBHK(B) is compared by other block hibrid collocation method in term of global error and step number. It is shown that KBHK(B) generates minimum global error with minimum step number.

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