On the Integration of Stiff ODEs Using Block Backward Differentiation Formulas of Order Six

被引：11
|
作者：
Nasarudin, Amiratul Ashikin [1 ]
Ibrahim, Zarina Bibi [2 ]
Rosali, Haliza [1 ]
机构：
[1] Fac Sci, Dept Math, Serdang 43400, Upm, Malaysia
[2] Fac Sci, Inst Math Res, Dept Math, Serdang 43400, Upm, Malaysia
来源：
SYMMETRY-BASEL | 2020年 / 12卷 / 06期
关键词：
fully implicit; block backward differentiation formula; off-step point;
D O I：
10.3390/sym12060952
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：
In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6)), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.
引用
收藏
页数：13
相关论文
共 50 条
  • [21] On the Convergence of Backward Differentiation Formulas for Stiff Initial Value Problems
    Gabriela Kirlinger
    BIT Numerical Mathematics, 2001, 41 : 1039 - 1048
  • [22] On the convergence of backward differentiation formulas for stiff initial value problems
    Kirlinger, G
    BIT, 2001, 41 (05): : 1039 - 1048
  • [23] Stability of Block Backward Differentiation Formulas Method
    Nasir, Nor Ain Azeany Mohd
    Ibrahim, Zarina Bibi
    Suleiman, Mohamed
    Othman, Khairil Iskandar
    22ND NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM22), 2015, 1682
  • [24] Stability Analysis of Singly Diagonally Implicit Block Backward Differentiation Formulas for Stiff Ordinary Differential Equations
    Aksah, Saufianim Jana
    Ibrahim, Zarina Bibi
    Zawawi, Iskandar Shah Mohd
    MATHEMATICS, 2019, 7 (02)
  • [25] 2ND DERIVATIVE EXTENDED BACKWARD DIFFERENTIATION FORMULAS FOR THE NUMERICAL-INTEGRATION OF STIFF SYSTEMS
    CASH, JR
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 1981, 18 (01) : 21 - 36
  • [26] Block Method for Generalised Multistep Adams and Backward Differentiation Formulae In Solving First Order ODEs
    Ibrahim, Zarina Bibi
    Suleiman, Mohamed
    Iskandar, Khairil
    Majid, Zanariah
    MATEMATIKA, 2005, 21 (01) : 25 - 33
  • [27] The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids
    Abdi, Ali
    Hosseini, Seyyed Ahmad
    Podhaisky, Helmut
    NUMERICAL ALGORITHMS, 2025, 98 (02) : 877 - 902
  • [28] Direct block backward differentiation formulas for solving second order ordinary differential equations
    Ibrahim, Zarina Bibi
    Suleiman, Mohamed
    Othman, Khairil Iskandar
    International Journal of Computational and Mathematical Sciences, 2009, 3 (03): : 120 - 122
  • [29] Direct block backward differentiation formulas for solving second order ordinary differential equations
    Ibrahim, Zarina Bibi
    Suleiman, Mohamed
    Othman, Khairil Iskandar
    World Academy of Science, Engineering and Technology, 2009, 40 : 57 - 59
  • [30] Direct Fifth Order Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations
    Zainuddin, Nooraini
    Ibrahim, Zarina Bibi
    Othman, Khairil Iskandar
    Suleiman, Mohamed
    CHIANG MAI JOURNAL OF SCIENCE, 2016, 43 (05): : 1170 - 1180
12345