Journal of the Korean Society for Industrial and Applied Mathematics

  • 제26권4호
  • /
  • Pages.353-361
  • /
  • 2022
  • /
  • 1226-9433(pISSN)
  • /
  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

A WEIGHTED EULER METHOD FOR SOLVING STIFF INITIAL VALUE PROBLEMS

  • BEONG IN, YUN (DEPARTMENT OF MATHEMATICS, KUNSAN NATIONAL UNIVERSITY)
  • 투고 : 2022.12.08
  • 심사 : 2022.12.19
  • 발행 : 2022.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

For an initial value problem, using a weighted average between two adjacent approximates, we propose a simple one-step method based on the Euler method. This method is useful for solving stiff initial value problem, even when the step size is not very small. Moreover, it can be seen that the proposed method with some selected weights results in improved approximation errors.

키워드

과제정보

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) [No. 2021R1F1A1047343].

참고문헌

  1. K.A. Atkinson, An Introduction to Numerical Analysis, 2nd edition, John Wiley & Sons, 1989
  2. R.L. Burden, J.D. Faires, Numerical Analysis, Brooks/Cole Pub., 1997
  3. J.C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, 2003
  4. D.F. Griffiths, D.J. Higham, Numerical methods for ordinary differential equations, Springer Undergraduate Mathematics Series, Springer London, 2010.
  5. R. Kress, Numerical Analysis Brooks/Cole Publishing Company, Springer, New York, 1998
  6. A. Guzel, W. Layton, Time filters increase accuracy of the fully implicit method, BIT Numerical Mathematics, 58 (2018), 301-315. https://doi.org/10.1007/s10543-018-0695-z
  7. O. Koch, P. Kofler, E.B. Weinmuller, The implicit Euler method for the numerical solution of singular initial value problems, Applied Numerical Mathematics, 34 (2000), 231-252. https://doi.org/10.1016/S0168-9274(99)00130-0
  8. K.H. Mohammad, S.A. Mohammad, A.H. Mohammad, A.S. Mohamma, B.H. Mohammad, An Implicit Method for Numerical Solution of Second Order Singular Initial Value Problems, The Open Mathematics Journal, 7 (2014), 1-5.
  9. A.M. Wazwaz, A new method for solving singular initial value problems in the second- order ordinary differential equations, Applied Mathematics and Computations, 28 (2002), 45-57. https://doi.org/10.1016/S0096-3003(01)00021-2
  10. B.I. Yun, An improved implicit Euler method for solving initial value problems, Journal of the Korean Society for Industrial and Applied Mathematics, 26 (2022), 138-155.
  11. Wikipedia, Stiff equation, http://en.wikipedia.org/wiki/Stiffequation#A-stability.
  12. Wikipedia, Backward differentiation formula, http://en.wikipedia.org/wiki/Backward_differentiation_formula.
  13. R.J. LeVeque, Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, Society for Industrial and Applied Mathematics, Philadelphia, 2007.