N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

X. M. Liu, H. Y Zhang, and Y. L Guo, “A novel method for Raman amplifier propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).

[Crossref]

T. Mizuochi, K. Kinjo, S. Kajiya, T. Tokura, and K. Motoshima, “Bidirectional unrepeatered 43 Gb/s WDM transmission with C/L band-separated Raman amplification,” J. Lightwave Technol. 20, 2079–2085 (2002).

[Crossref]

E. M. Dianov, “Advances in Raman fibers,” J. Lightwave Technol. 20, 1457–1462 (2002).

[Crossref]

M. Karásek and M. Menif, “Channel addition/removal response in Raman fiber amplifiers: modeling and experimentation,” J. Lightwave Technol. 20, 1680–1687 (2002).

[Crossref]

V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20, 250–254 (2002).

[Crossref]

A. Carena, V. Curri, and P. Poggiolini, “On the optimization of hybrid Raman/erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 13, 1170–1172 (2001).

[Crossref]

Q. H. Mao, J. S. Wang, X. H. Sun, and M. D. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifiers with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).

[Crossref]

W. H. Enright and P. H. Muir, “Runge-Kutta software with defect control for boundary value ODEs,” SIAM J. Sci. Comput. 17, 479–497 (1996).

[Crossref]

R. Weiss, “The application of implicit Runge-Kutta and collocation methods to boundary value problems,” Math. Comp. 28, 449–464 (1974).

U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (SIAM, Philadelphia, 1998).

[Crossref]

U. M. Ascher, R. M. M. Mattheij, and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (SIAM, Philadelphia, 1995).

[Crossref]

P. B. Bailey, L. F. Shampine, and P. E. Waltman, Nonlinear Two Point Boundary Value Problems (Academic Press, New York, 1968).

A. Carena, V. Curri, and P. Poggiolini, “On the optimization of hybrid Raman/erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 13, 1170–1172 (2001).

[Crossref]

A. Carena, V. Curri, and P. Poggiolini, “On the optimization of hybrid Raman/erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 13, 1170–1172 (2001).

[Crossref]

W. H. Enright and P. H. Muir, “Runge-Kutta software with defect control for boundary value ODEs,” SIAM J. Sci. Comput. 17, 479–497 (1996).

[Crossref]

X. M. Liu, H. Y Zhang, and Y. L Guo, “A novel method for Raman amplifier propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

X. M. Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” (to be submitted)

X. M. Liu and B. Lee, “A series of fast and accurate algorithms and their applications in fiber transmission systems,” (submitted to IEEE J. Quantum Electron.)

X. M. Liu, H. Y Zhang, and Y. L Guo, “A novel method for Raman amplifier propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).

[Crossref]

X. M. Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” (to be submitted)

X. M. Liu and B. Lee, “A series of fast and accurate algorithms and their applications in fiber transmission systems,” (submitted to IEEE J. Quantum Electron.)

Q. H. Mao, J. S. Wang, X. H. Sun, and M. D. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifiers with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

J. H. Mathews, Numerical Methods for Mathematics, Science, and Engineering (Second edition, Prentice Hall, New Jersey, 1992), pp. 464–475.

U. M. Ascher, R. M. M. Mattheij, and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (SIAM, Philadelphia, 1995).

[Crossref]

W. H. Enright and P. H. Muir, “Runge-Kutta software with defect control for boundary value ODEs,” SIAM J. Sci. Comput. 17, 479–497 (1996).

[Crossref]

U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (SIAM, Philadelphia, 1998).

[Crossref]

B. F. Plybon, An Introduction to Applied Numerical Analysis (PWS-KENT Publishing Company, Boston, 1992), pp. 428–441.

A. Carena, V. Curri, and P. Poggiolini, “On the optimization of hybrid Raman/erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 13, 1170–1172 (2001).

[Crossref]

A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics (Springer-Verlag, New York, 2000).

U. M. Ascher, R. M. M. Mattheij, and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (SIAM, Philadelphia, 1995).

[Crossref]

A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics (Springer-Verlag, New York, 2000).

A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics (Springer-Verlag, New York, 2000).

L. F. Shampine, Numerical Solution of Ordinary Differential Equations (Chapman & Hall, New York, 1994).

P. B. Bailey, L. F. Shampine, and P. E. Waltman, Nonlinear Two Point Boundary Value Problems (Academic Press, New York, 1968).

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

Q. H. Mao, J. S. Wang, X. H. Sun, and M. D. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifiers with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

P. B. Bailey, L. F. Shampine, and P. E. Waltman, Nonlinear Two Point Boundary Value Problems (Academic Press, New York, 1968).

Q. H. Mao, J. S. Wang, X. H. Sun, and M. D. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifiers with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).

[Crossref]

R. Weiss, “The application of implicit Runge-Kutta and collocation methods to boundary value problems,” Math. Comp. 28, 449–464 (1974).

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

X. M. Liu, H. Y Zhang, and Y. L Guo, “A novel method for Raman amplifier propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).

[Crossref]

Q. H. Mao, J. S. Wang, X. H. Sun, and M. D. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifiers with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).

[Crossref]

X. M. Liu, H. Y Zhang, and Y. L Guo, “A novel method for Raman amplifier propagation equations,” IEEE Photon. Technol. Lett. 15, 392–394 (2003).

[Crossref]

A. Carena, V. Curri, and P. Poggiolini, “On the optimization of hybrid Raman/erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 13, 1170–1172 (2001).

[Crossref]

N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, “Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 27–29 (2003).

[Crossref]

T. Mizuochi, K. Kinjo, S. Kajiya, T. Tokura, and K. Motoshima, “Bidirectional unrepeatered 43 Gb/s WDM transmission with C/L band-separated Raman amplification,” J. Lightwave Technol. 20, 2079–2085 (2002).

[Crossref]

E. M. Dianov, “Advances in Raman fibers,” J. Lightwave Technol. 20, 1457–1462 (2002).

[Crossref]

M. Karásek and M. Menif, “Channel addition/removal response in Raman fiber amplifiers: modeling and experimentation,” J. Lightwave Technol. 20, 1680–1687 (2002).

[Crossref]

V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20, 250–254 (2002).

[Crossref]

R. Weiss, “The application of implicit Runge-Kutta and collocation methods to boundary value problems,” Math. Comp. 28, 449–464 (1974).

Q. H. Mao, J. S. Wang, X. H. Sun, and M. D. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifiers with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).

[Crossref]

W. H. Enright and P. H. Muir, “Runge-Kutta software with defect control for boundary value ODEs,” SIAM J. Sci. Comput. 17, 479–497 (1996).

[Crossref]

X. M. Liu and B. Lee, “A series of fast and accurate algorithms and their applications in fiber transmission systems,” (submitted to IEEE J. Quantum Electron.)

X. M. Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” (to be submitted)

U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (SIAM, Philadelphia, 1998).

[Crossref]

A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics (Springer-Verlag, New York, 2000).

B. F. Plybon, An Introduction to Applied Numerical Analysis (PWS-KENT Publishing Company, Boston, 1992), pp. 428–441.

J. H. Mathews, Numerical Methods for Mathematics, Science, and Engineering (Second edition, Prentice Hall, New Jersey, 1992), pp. 464–475.

U. M. Ascher, R. M. M. Mattheij, and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (SIAM, Philadelphia, 1995).

[Crossref]

P. B. Bailey, L. F. Shampine, and P. E. Waltman, Nonlinear Two Point Boundary Value Problems (Academic Press, New York, 1968).

L. F. Shampine, Numerical Solution of Ordinary Differential Equations (Chapman & Hall, New York, 1994).