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Simple yet highly efficient numerical techniques for systems of nonlinear equations

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Abstract

For solving nonlinear equations, two multi-step iterative methods with fifth and seventh order of convergence are presented and analyzed. Keeping in mind the idea of high computational efficiency, the methods are constructed using only two Jacobian matrices and one matrix inversion per iteration, apart from three and four functional evaluations corresponding to the fifth- and seventh-order methods. The efficiency index is determined and compared with the existing methods of similar nature. The numerical testing is executed using the high precision arithmetic to demonstrate the performance of techniques on diverse practical problems. The results obtained are remarkable in the sense that new methods are highly efficient compared to the existing counterparts, particularly in the case of large scale systems.

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Authors and Affiliations

  1. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, 148106, India

    Harmandeep Singh & Janak Raj Sharma

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  1. Harmandeep Singh
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  2. Janak Raj Sharma
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Correspondence to Janak Raj Sharma.

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Communicated by Jose Alberto Cuminato.

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Singh, H., Sharma, J.R. Simple yet highly efficient numerical techniques for systems of nonlinear equations. Comp. Appl. Math. 42, 22 (2023). https://doi.org/10.1007/s40314-022-02159-9

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  • DOI: https://doi.org/10.1007/s40314-022-02159-9

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