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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.17 No.4
- 발행연도
- 2013.12
- 수록면
- 221 - 237 (17page)
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초록· 키워드
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In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction?diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.
목차
ABSTRACT
1. INTRODUCTION
2. STATEMENT OF THE PROBLEM
3. STABILITY RESULT
4. AN ASYMPTOTIC EXPANSION
5. NUMERICAL METHODS
6. AN ERROR ESTIMATE
7. DISCONTINUOUS SOURCE TERM
8. NUMERICAL RESULTS
9. DISCUSSION
REFERENCES
참고문헌 (24)
참고문헌 신청
1. [단행본] - Thomas Erneux / 2009 / Applied Delay Differential Equations / Springer
2. [학술지(정기간행물)] - A. Longtin / 1988 / Complex oscillations in the human pupil light reflex with mixed and delayed feedback / Math. Biosci 90 : 183 ~ 199
3. [학술지(정기간행물)] - C. G. Lange / 1994 / Singular perturbation analysis of boundary-value problems for differentialdifference equations V. Small shifts with layer behavior / SIAM. J. APPL. MATH 54 (1) : 249 ~ 272
4. [학술지(정기간행물)] - M.W. Derstine / 1982 / Bifurcation gap in a hybrid optical system / Phys. Rev. A. 26 : 3720 ~ 3722
5. [학술지(정기간행물)] - V.Y. Glizer / 2003 / Asymptotic analysis and solution of a finite-horizon H∞ control problem for singularly-perturbed linear systems with small state delay / J. Optim. Theory Appl 117 : 295 ~ 325
2. [학술지(정기간행물)] - A. Longtin / 1988 / Complex oscillations in the human pupil light reflex with mixed and delayed feedback / Math. Biosci 90 : 183 ~ 199
3. [학술지(정기간행물)] - C. G. Lange / 1994 / Singular perturbation analysis of boundary-value problems for differentialdifference equations V. Small shifts with layer behavior / SIAM. J. APPL. MATH 54 (1) : 249 ~ 272
4. [학술지(정기간행물)] - M.W. Derstine / 1982 / Bifurcation gap in a hybrid optical system / Phys. Rev. A. 26 : 3720 ~ 3722
5. [학술지(정기간행물)] - V.Y. Glizer / 2003 / Asymptotic analysis and solution of a finite-horizon H∞ control problem for singularly-perturbed linear systems with small state delay / J. Optim. Theory Appl 117 : 295 ~ 325
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