Variable Order Block Method for Solving Second Order Ordinary Differential Equations

被引：9

作者：

Ibrahim, Zarina Bibi ^{[1
,2
]}

Zainuddin, Nooraini ^{[3
]}

Othman, Khairil Iskandar ^{[4
]}

Suleiman, Mohamed ^{[2
]}

Zawawi, Iskandar Shah Mohd ^{[5
]}

机构：

[1] Univ Putra Malaysia, Fac Sci, Dept Math, Upm Serdang 43400, Selangor Darul, Malaysia

[2] Univ Putra Malaysia, Inst Math Res, Upm Serdang 43400, Selangor Darul, Malaysia

[3] UTP, Dept Fundamental & Appl Sci, Bandar Seri Iskandar 32610, Perak Darul Rid, Malaysia

[4] Univ Teknol MARA, Fac Comp & Math Sci, Dept Math, Shah Alam 40450, Selangor Darul, Malaysia

[5] Univ Teknol MARA, Fac Comp & Math Sci, Seremban Campus, Seremban 70300, Negeri Sembilan, Malaysia

来源：

SAINS MALAYSIANA | 2019年 / 48卷 / 08期

关键词：

Block method; initial value problem; second order ODEs; variable order; NUMERICAL-INTEGRATION; MULTISTEP METHOD; FORMULA;

D O I：

10.17576/jsm-2019-4808-23

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper proposed 2-point block backward differentiation formulas (BBDF) of order 3, 4, and 5 for direct solution of second order ordinary differential equations. These methods were derived via backward difference interpolation polynomial with two solutions are produced simultaneously at each step. All the three different orders of 2-point BBDF is implemented in variable order scheme. The scheme utilizes the local truncation error, which is generated by the single order of 2-point BBDF method. Numerical results are presented to illustrate the validity of the proposed scheme.

引用

页码：1761 / 1769

页数：9

共 21 条

[1] FAMILIES OF 3-STAGE 3RD ORDER RUNGE-KUTTA-NYSTROM METHODS FOR Y''=F(X,Y,Y') [J].

CHAWLA, MM ;

SHARMA, SR .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1985, 26 (JAN) :375-386

[2] Solution of Third Order Ordinary Differential Equation using Improved Block Hybrid Collocation Method [J].

Chien, Lee Khai ;

Din, Ummul Khair Salma ;

Ahmad, Rokiah Rozita .

SAINS MALAYSIANA, 2018, 47 (09) :2179-2186

[3] A NEW NUMERICAL-METHOD FOR THE INTEGRATION OF HIGHLY OSCILLATORY 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATIONS [J].

DENK, G .

APPLIED NUMERICAL MATHEMATICS, 1993, 13 (1-3) :57-67

[4] A robust trigonometrically fitted embedded pair for perturbed oscillators [J].

Fang, Yonglei ;

Song, Yongzhong ;

Wu, Xinyuan .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (02) :347-355

[5] BLOCK METHODS FOR 2ND-ORDER ODES [J].

FATUNLA, SO .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1991, 41 (1-2) :55-63

[6] NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS [J].

GEAR, CW .

MATHEMATICS OF COMPUTATION, 1967, 21 (98) :146-&

[7]

Henrici P., 1962, Discrete variable methods in ordinary differential equations

[8] Implicit r-point block backward differentiation formula for solving first-order stiff ODEs [J].

Ibrahim, Zarina Bibi ;

Othman, Khairil Iskandar ;

Suleiman, Mohamed .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) :558-565

[9]

Ibrahim ZB, 2012, CHIANG MAI J SCI, V39, P502

[10] Block Hybrid Method with Trigonometric-Fitting for Solving Oscillatory Problems [J].

Ismail, Fudziah ;

Ahmad, Sufia Zulfa ;

Jikantoro, Yusuf Dauda ;

Senu, Norazak .

SAINS MALAYSIANA, 2018, 47 (09) :2223-2230

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