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Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations
Joint Authors
Liu, M. Y.
Zhang, L.
Zhang, C. F.
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-10-10
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The implicit Runge–Kutta method with A-stability is suitable for solving stiff differential equations.
However, the fully implicit Runge–Kutta method is very expensive in solving large system problems.
Although some implicit Runge–Kutta methods can reduce the cost of computation, their accuracy and stability are also adversely affected.
Therefore, an effective banded implicit Runge–Kutta method with high accuracy and high stability is proposed, which reduces the computation cost by changing the Jacobian matrix from a full coefficient matrix to a banded matrix.
Numerical solutions and results of stiff equations obtained by the methods involved are compared, and the results show that the banded implicit Runge–Kutta method is advantageous to solve large stiff problems and conducive to the development of simulation.
American Psychological Association (APA)
Liu, M. Y.& Zhang, L.& Zhang, C. F.. 2019. Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-8.
https://search.emarefa.net/detail/BIM-1195795
Modern Language Association (MLA)
Liu, M. Y.…[et al.]. Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations. Mathematical Problems in Engineering No. 2019 (2019), pp.1-8.
https://search.emarefa.net/detail/BIM-1195795
American Medical Association (AMA)
Liu, M. Y.& Zhang, L.& Zhang, C. F.. Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-8.
https://search.emarefa.net/detail/BIM-1195795
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195795