A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations

Date

2009-04-15

Author

Tarman, Işık Hakan

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A novel algorithm implementing Chebyshev spectral collocation (pseudospectral) method in combination with Newton's method is proposed for the nonlinear two-point boundary value problem (BVP) arising in solving propagation equations in fiber Raman amplifier. Moreover, an algorithm to train the known linear solution for use as a starting solution for the Newton iteration is proposed and successfully implemented. The exponential accuracy obtained by the proposed Chebyshev pseudospectral method is demonstrated on a case of the Raman propagation equations with strong nonlinearities. This is in contrast to algebraic accuracy obtained by typical solvers used in the literature. The resolving power and the efficiency of the underlying Chebyshev grid are demonstrated in comparison to a known BVP solver.

Subject Keywords

Physical and Theoretical Chemistry, Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials

URI

https://hdl.handle.net/11511/35926

Journal

OPTICS COMMUNICATIONS

DOI

https://doi.org/10.1016/j.optcom.2008.11.092

Collections

Department of Mechanical Engineering, Article

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Citation Formats

I. H. Tarman, “A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations,” OPTICS COMMUNICATIONS, pp. 1551–1556, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35926.