Numerical Solver of A(alpha)-stable for Stiff Ordinary Differential Equations

被引：0

作者：

Jusoh, Rahimah ^{[1
]}

Aksah, Saufianim J. ^{[2
]}

Zainuddin, Nooraini ^{[3
]}

Ibrahim, Zarina B. ^{[4
]}

机构：

[1] Univ Malaysia Pahang, Ctr Math Sci, Kuantan 26300, Pahang, Malaysia

[2] Univ Teknol MARA, Ctr Fdn Studies, Kampus Dengkil, Dengkil 43800, Selangor, Malaysia

[3] Univ Teknol PETRONAS, Dept Fundamental & Appl Sci, Bandar Seri Iskandar 36210, Perak, Malaysia

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

来源：

ENGINEERING LETTERS | 2023年 / 31卷 / 04期

关键词：

singly diagonally implicit; block multistep method; A(alpha) - stable; stiff ODEs;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, a numerical solver for stiff ordinary differential equations (ODEs) known as the Extended Singly Diagonally Implicit Block Backward Differentiation Formulas (ESDIBDDF) is developed. Objectives of this study are to analyse the A(alpha) - stability of the ESDIBBDF method and enhance its accuracy by employing a strategy that minimizes the error norm to optimize the values of free parameters. In addition to that, accuracy of the method is to be enhanced by approximating solutions by implementing extra functions to be evaluated. The formula is specifically designed in a lower triangular form with equal diagonal coefficients, enabling faster computation of numerical solutions. Numerical experiments are conducted to assess the efficiency of this method as a solver for stiff ODEs, comparing it with existing methods. The A(alpha) - stability analysis is verified and conditions for convergence are discussed. The conclusive works efficiently as an alternate solver for stiff ODEs. The research recommended extended application of the developed method to solve applied problems.

引用

页码：1574 / 1583

页数：10

共 50 条

[1] A HIGHLY ACCURATE SOLVER FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS
Kushnir, Dan
Rokhlin, Vladimir
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (03): : A1296 - A1315
[2] A class of A(α)-stable numerical methods for stiff problems in ordinary differential equations
Okuonghae R.I.
[J]. Numerical Analysis and Applications, 2013, 6 (4) : 298 - 313
[3] Stable Integration of Stiff Random Ordinary Differential Equations
Asai, Y.
Herrmann, E.
Kloeden, P. E.
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2013, 31 (02) : 293 - 313
[4] The numerical simulation for stiff systems of ordinary differential equations
Darvishi, M. T.
Khani, F.
Soliman, A. A.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (7-8) : 1055 - 1063
[5] A Numerical Algorithm for Solving Stiff Ordinary Differential Equations
Yatim, S. A. M.
Ibrahim, Z. B.
Othman, K. I.
Suleiman, M. B.
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
[6] SOME A-STABLE METHODS FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS
JAIN, RK
[J]. MATHEMATICS OF COMPUTATION, 1972, 26 (117) : 71 - &
[7] NUMERICAL DIFFERENTIATION FORMULAS FOR STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
KLOPFENSTEIN, RW
[J]. RCA REVIEW, 1971, 32 (03): : 447 - +
[8] REVIEW OF NUMERICAL INTEGRATION TECHNIQUES FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS
SEINFELD, JH
LAPIDUS, L
HWANG, M
[J]. INDUSTRIAL & ENGINEERING CHEMISTRY FUNDAMENTALS, 1970, 9 (02): : 266 - &
[9] NUMERICAL-SOLUTION OF SYSTEMS OF STIFF ORDINARY DIFFERENTIAL EQUATIONS
CASH, JR
[J]. PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1974, 76 (SEP): : 443 - 456
[10] On stable integration of stiff ordinary differential equations with global error control
Kulikov, GY
Shindin, SK
[J]. COMPUTATIONAL SCIENCE - ICCS 2005, PT 1, PROCEEDINGS, 2005, 3514 : 42 - 49

← 1 2 3 4 5 →