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Finite-difference method for singular nonlinear systems

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Abstract

This paper presents a method for solving nonlinear system with singular Jacobian at the solution. The convergence rate in the case of singularity deteriorates and one way to accelerate convergence is to form bordered system. A local algorithm, with finite-difference approximations, for forming and solving such system is proposed in this paper. To overcome the need that initial approximation has to be very close to the solution, we also propose a method which is a combination of descent method with finite-differences and local algorithm. Some numerical results obtained on relevant examples are presented.

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Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, Department of Fundamental Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000, Novi Sad, Serbia

    Sandra Buhmiler, Slavica Medić & Tatjana Grbić

  2. Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 3, 21000, Novi Sad, Serbia

    Sanja Rapajić

Authors
  1. Sandra Buhmiler
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  2. Sanja Rapajić
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  3. Slavica Medić
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  4. Tatjana Grbić
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Corresponding author

Correspondence to Sanja Rapajić.

Additional information

This work is partially supported by Ministry of Education, Science and Technological Development, Republic of Serbia, grants no. 174030, 174009, TR32035 and the Project 142-451-2489 of the Provincial Secretariat for Higher Education and Scientific Research.

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Buhmiler, S., Rapajić, S., Medić, S. et al. Finite-difference method for singular nonlinear systems. Numer Algor 79, 65–86 (2018). https://doi.org/10.1007/s11075-017-0428-4

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  • DOI: https://doi.org/10.1007/s11075-017-0428-4

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