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A Spectral Quasilinearization Parametric Method for Nonlinear Two-Point Boundary Value Problems

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Abstract

In this paper, we develop an efficient explicit method based on the spectral parametric iteration method and quasilinearization scheme, which can be used for the efficient numerical solution of nonlinear stiff/nonstiff two-point boundary value problems. The method derived here has the advantage that it does not require the solution of nonlinear systems of equations. We derive the method, which requires one evaluation of the Jacobian and one LU decomposition per step. Some numerical experiments on nonlinear stiff/nonstiff problems show the efficiency and accuracy of the method. Moreover, the method provides us a simple way to control and modify the convergence rate of the solution.

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Acknowledgements

This research was supported by a grant from Ferdowsi University of Mashhad (No. 2/42583). Further, the authors are very grateful to the editor and referees for their comments and suggestions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Asghar Ghorbani & Morteza Gachpazan

Authors
  1. Asghar Ghorbani
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  2. Morteza Gachpazan
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Correspondence to Asghar Ghorbani.

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Communicated by Mohammad Sal Moslehian.

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Ghorbani, A., Gachpazan, M. A Spectral Quasilinearization Parametric Method for Nonlinear Two-Point Boundary Value Problems. Bull. Malays. Math. Sci. Soc. 42, 1–13 (2019). https://doi.org/10.1007/s40840-017-0467-y

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  • DOI: https://doi.org/10.1007/s40840-017-0467-y

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