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Peer-reviewedCC BY 4.0Mathematics

A Class of Higher-Order Iterative Methods for Simultaneous Solutions of Nonlinear Equations with Applications to Biological Problems

  • Monika Panwar1
  • Sonia Bhalla1
  • Ramandeep Behl2
  • Paula Triguero-Navarro3
  • Alicia Cordero3
  • Juan R. Torregrosa3
  1. 1Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, India
  2. 2Department of Mathematical Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
  3. 3Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain
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Abstract

A new class of high-order simultaneous iterative methods is constructed for the simultaneous computation of all simple roots of a nonlinear equation. The objective is to develop efficient iterative schemes with improved convergence characteristics and computational performance. The schemes are constructed by applying suitable weight functions and attain a convergence order of 2p+1, where p denotes the order of the predictor iterative method. Their performance is investigated through comprehensive numerical experiments on several nonlinear biological models, including the Population Model with Allee Effect and Density–Dependent Migration, the Epidemic Disease Model, and the Michaelis–Menten Enzyme Kinetics Model, to illustrate the accuracy, efficiency, and convergence behavior of the proposed schemes. Additionally, error graphs are plotted to compare the proposed methods with existing methods. The numerical results show that some of the proposed schemes achieve faster convergence and lower residual errors than existing schemes and have better computational performance. The results indicate that the proposed methods are competitive and reliable for solving nonlinear equations arising in biological and applied mathematical models.

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Cite

BibTeXRIS
BibTeX
@article{panwar2026class,
  title = {{A Class of Higher-Order Iterative Methods for Simultaneous Solutions of Nonlinear Equations with Applications to Biological Problems}},
  author = {Monika Panwar and Sonia Bhalla and Ramandeep Behl and Paula Triguero-Navarro and Alicia Cordero and Juan R. Torregrosa},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213871},
  url = {https://www.mdpi.com/2227-7390/14/21/3871},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Class of Higher-Order Iterative Methods for Simultaneous Solutions of Nonlinear Equations with Applications to Biological Problems
AU  - Monika Panwar
AU  - Sonia Bhalla
AU  - Ramandeep Behl
AU  - Paula Triguero-Navarro
AU  - Alicia Cordero
AU  - Juan R. Torregrosa
PY  - 2026
DA  - 2026/10/23
JO  - Mathematics
DO  - 10.3390/math14213871
UR  - https://www.mdpi.com/2227-7390/14/21/3871
AB  - A new class of high-order simultaneous iterative methods is constructed for the simultaneous computation of all simple roots of a nonlinear equation. The objective is to develop efficient iterative schemes with improved convergence characteristics and computational performance. The schemes are constructed by applying suitable weight functions and attain a convergence order of 2p+1, where p denotes the order of the predictor iterative method. Their performance is investigated through comprehensive numerical experiments on several nonlinear biological models, including the Population Model with Allee Effect and Density–Dependent Migration, the Epidemic Disease Model, and the Michaelis–Menten Enzyme Kinetics Model, to illustrate the accuracy, efficiency, and convergence behavior of the proposed schemes. Additionally, error graphs are plotted to compare the proposed methods with existing methods. The numerical results show that some of the proposed schemes achieve faster convergence and lower residual errors than existing schemes and have better computational performance. The results indicate that the proposed methods are competitive and reliable for solving nonlinear equations arising in biological and applied mathematical models.
SN  - 2227-7390
ER  -