International Journal of Numerical Methods and Applications

The International Journal of Numerical Methods and Applications publishes research articles on numerical methods and their applications in various fields, including differential equations, fluid dynamics, and bioinformatics. It also welcomes survey articles on new methods in numerical analysis.

Submit Article

ON THE CONVERGENCE OF NEWTON’S METHOD COMBINED WITH A PROXIMAL APPROACH FOR AN EIGENVALUE PROBLEM - A CORRECTED VERSION

Authors

  • Fabio Silva Botelho

Keywords:

eigenvalue model, partial differential equation, numerical method, Banach fixed point theorem, finite differences approach

DOI:

https://doi.org/10.17654/0975045225018

Abstract

This article develops a numerical method for solving a large class of eigenvalue problems for partial differential equations.

The main result is proved through an application of the Banach fixed point theorem.

Further, we present a numerical example and respective software for a Ginzburg-Landau type equation.

Received: July 1, 2025
Accepted: August 12, 2025

References

[1] F. Botelho, Functional Analysis and Applied Optimization in Banach Spaces, Springer, Switzerland, 2014.

[2] F. S. Botelho, Duality principles and numerical procedures for a large class of non-convex models in the calculus of variations, Preprints 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v95.

[3] F. S. Botelho, Duality principles and numerical procedures for a large class of non-convex models in the calculus of variations, Preprint, Preprints.org, 2025. DOI:10.20944/preprints202302.0051.v97.

[4] J. F. Annet, Superconductivity, superfluids and condensates, 2nd ed., Oxford Master Series in Condensed Matter Physics, Oxford University Press, Reprint, 2010.

[5] L. D. Landau and E. M. Lifschits, Course of theoretical physics, Vol. 5, Statistical Physics, Part 1, Butterworth-Heinemann, Elsevier, Reprint 2008.

[6] R. A. Adams and J. F. Fournier, Sobolev Spaces, 2nd ed., Elsevier, New York, 2003.

[7] J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd ed., SIAM, Philadelphia, 2004.

Downloads

Published

2025-08-23

Issue

Vol. 25 No. 2 (2025)

Section

Articles

License

Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Licensing Terms:

Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.

Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.

No Derivatives: Modifying or creating derivative works not allowed without written permission.

Contact Pushpa Publishing House for more info or permissions.

How to Cite

ON THE CONVERGENCE OF NEWTON’S METHOD COMBINED WITH A PROXIMAL APPROACH FOR AN EIGENVALUE PROBLEM - A CORRECTED VERSION. (2025). International Journal of Numerical Methods and Applications, 25(2), 443-455. https://doi.org/10.17654/0975045225018

Similar Articles

1-10 of 50

You may also start an advanced similarity search for this article.