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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제33권 제5호
- 발행연도
- 2015.1
- 수록면
- 657 - 670 (14page)
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In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.
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참고문헌 (21)
참고문헌 신청
R. Barrio / 1999 / On the A-stability of Runge-Kutta collocation methods based on orthogonal polynomials / SIAM J. Numer. Anal 36:1291~1303
R. Bellman. / 1971 / Differential quadrature and long-term integration / J. Math. Anal. Appl 34:235~238
C. W. Bert. / 1996 / Differential quadrature method in computational mechanics : a review / Appl. Mech. Rev 49:1~28
C. W. Bert. / 1993 / Differential quadrature for static and free vibration analyses of anisotropic plates / Inter. J. Solids Struct 30:1737~1744
J. C. Butcher / 1992 / The role of orthogonal polynomials in numerical differential equations / J. Comput. Appl. Math 43:231~242
R. Bellman. / 1971 / Differential quadrature and long-term integration / J. Math. Anal. Appl 34:235~238
C. W. Bert. / 1996 / Differential quadrature method in computational mechanics : a review / Appl. Mech. Rev 49:1~28
C. W. Bert. / 1993 / Differential quadrature for static and free vibration analyses of anisotropic plates / Inter. J. Solids Struct 30:1737~1744
J. C. Butcher / 1992 / The role of orthogonal polynomials in numerical differential equations / J. Comput. Appl. Math 43:231~242
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