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Successive iteration technique for singular nonlinear system with four-point boundary conditions

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Abstract

In this paper, the existence of at least one positive solution of the system of singular differential equations with four-point coupled boundary conditions is discussed. A constructive monotonic iterative technique on the equivalent completely continuous nonlinear operator is used to establish the result. This method produces an approximate solution in the form of series which is very helpful in developing a numerical scheme for the positive solution of the system. It is demonstrated through the examples.

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Acknowledgements

This work is supported by Science and Engineering Research Board, New Delhi (Grant No. ECR/2017/000560). We are thankful to the referees for valuable suggestions.

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  1. Department of Mathematics and Scientific Computing, MMM University of Technology, Gorakhpur, 273010, India

    Amit K. Barnwal & Priti Pathak

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  1. Amit K. Barnwal
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  2. Priti Pathak
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Correspondence to Amit K. Barnwal.

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Barnwal, A.K., Pathak, P. Successive iteration technique for singular nonlinear system with four-point boundary conditions. J. Appl. Math. Comput. 62, 301–324 (2020). https://doi.org/10.1007/s12190-019-01285-8

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  • DOI: https://doi.org/10.1007/s12190-019-01285-8

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